📚 Aptitude Practice Hub

Pavan X Dhee Coding Lab

20 carefully curated practice questions for each topic — no solutions, just pure practice to sharpen your skills.

📖 20 Topics ✍️ 500+ Questions 🎯 Self-Assessment

🧩Percentages

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
28 Practice Questions
📝 Practice Questions
  • 1 Rahul’s marks increased from 60 to 80 in mathematics. What is the percentage change?
  • 2 If Rahul’s marks changed from 50 to 30 in science, what is the percentage decrease?
  • 3 A number is increased by 20% and then again by 10%. What is the net percentage change?
  • 4 A number is increased by 10% and then decreased by 10%. What is the net percentage change?
  • 5 A number is decreased by 20% and then again decreased by 20%. What is the net percentage change?
  • 6 If a number is increased by 20%, by what percentage should it be decreased to return to the original?
  • 7 If a number is decreased by 20%, by what percentage should it be increased to return to the original?
  • 8 If Anirudh’s salary is 10% more than Vijay’s, by what percent is Vijay’s salary less than Anirudh’s?
  • 9 If Raj’s income is 25% less than Rahul’s, by what percent is Rahul’s income greater than Raj’s?
  • 10 Half of one third of one fifth of a number is 40. Find 80% of the number.
  • 11 15% of 45% of a number is 105.3. Find 24% of the number.
  • 12 If 25% of a number is added to 100, the result is the number itself. Find the number.
  • 13 If numerator increases by 20% and denominator by 25%, the fraction becomes 3/5. What is the original fraction?
  • 14 If 40% of a is b, then b% of 20 equals what in terms of a?
  • 15 An article priced at Rs 500 gets successive discounts of 20% and 40%. Find the selling price.
  • 16 The final price is Rs 448 after discounts of 20% and 30%. Find the original price.
  • 17 Three successive discounts of 10%, 15% and 20% are equivalent to a single discount of what percent?
  • 18 Out of 1200 boys and 800 girls, 40% boys and 20% girls failed. What percentage passed?
  • 19 If 60% boys and 55% girls passed and overall pass is 58%, find ratio of boys to girls.
  • 20 Out of 250 questions, Praveen got 40% of first 125 correct. How many must he get correct in remaining to reach 60% overall?
  • 21 Raj spends 25% on groceries, 20% on bills and 15% on travel. If he saves Rs 112000 annually, find his monthly salary.
  • 22 Shekhar spends 50% on groceries, 10% on travel and 20% of remaining on girlfriend. If he saves Rs 16000, find his income.
  • 23 Rajesh invested 20% more than Somesh. Somesh invested 10% less than Kunal. Total is Rs 17880. Find Kunal’s investment.
  • 24 Fresh fruit has 64% water, dried fruit 20%. From 100 kg fresh, how much dried fruit is obtained?
  • 25 Coins of 25p, 50p and 1 Rs are in ratio 10:5:2. Total value Rs 1400. Find total number of coins.
  • 26 Rahul bought 12 dozens toys at Rs 300 per dozen and sold each at Rs 50. Find profit percentage.
  • 27 A shopkeeper buys toffees at 6 for Rs 1. How many should he sell per rupee to gain 20%?
  • 28 If selling price is doubled and profit triples, find the profit percent.

🧩Profit and Loss

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
25 Practice Questions
📝 Practice Questions
  • 1 Vineet buys 6 mangoes for Rs 8 and sells them at 4 for Rs 6. Find his profit or loss percentage.
  • 2 Vineet buys mangoes at 4 kg for Rs 28 and sells them at 6 kg for Rs 60. To earn Rs 108 profit, how many kg should he sell?
  • 3 Ajay loses Rs 60 if he sells mangoes at Rs 6 each but gains Rs 65 if he sells them at Rs 6.25. How many mangoes does he sell?
  • 4 Vijay buys mangoes at Rs 5 per dozen and equal quantity at Rs 4 per dozen. He sells at Rs 5.5 per dozen and gains Rs 50. How many dozens did he buy?
  • 5 Vineet buys equal number of mangoes at 50 for Rs 10 and 40 for Rs 10. He sells them at 90 for Rs 20. Find his profit or loss percentage.
  • 6 If cost of 6 apples equals selling price of 8 apples, find profit or loss percentage.
  • 7 If cost of 8 apples equals selling price of 6 apples, find profit or loss percentage.
  • 8 Cost price of 20 apples equals selling price of x apples. If profit is 25%, find x.
  • 9 By selling 45 apples a man gains the selling price of 30 apples. Find profit percentage.
  • 10 Shankar sells at cost price but gives 900 g instead of 1 kg. Find his profit percentage.
  • 11 If Shankar also cheats supplier by taking 1100 g per kg, find his profit percentage.
  • 12 Kanak bought 2 bikes at Rs 1200 each. One sold at 20% profit and other at 10% loss. Find net profit or loss.
  • 13 Kanak bought 2 bikes at Rs 1200 each. One sold at 20% profit and other at 20% loss. Find net profit or loss.
  • 14 Kanak sold 2 bikes at Rs 1800 each. One sold at 20% profit and other at 10% loss. Find net profit or loss percentage.
  • 15 Kanak sold 2 bikes at Rs 1200 each. One sold at 20% profit and other at 20% loss. Find net profit or loss.
  • 16 After giving 12.5% discount, Ajay still gains 16.66%. Find the marked price percentage above cost price.
  • 17 Ajay bought a rucksack for Rs 4000 and sold at 18% loss. With that money he bought a cooker and sold at 20% profit. Find overall profit or loss.
  • 18 Ajay marks goods to gain 40% and gives 15% discount. Find actual profit percentage.
  • 19 Mahesh’s sales increase by 30% weekly. Difference between week 1 and week 3 is Rs 828. Find week 2 sales.
  • 20 Overall profit in 3 weeks is 71%. First and second week profits are 25% and 20%. Find third week profit.
  • 21 Milkman buys milk at x Rs/litre and sells at 3x Rs/litre, mixing 2L water per 10L milk. Find overall profit.
  • 22 After reducing MP by Rs 32, a shopkeeper still gains 15%. CP = Rs 320. Find profit if sold at MP.
  • 23 If selling price doubles and profit triples, find profit percentage.
  • 24 Selling 20 balls for Rs 1500 results in loss equal to CP of 5 balls. Find cost price per ball.
  • 25 A shopkeeper gains 25% and uses 25% less weight. Find total profit percentage.
  • 💡 Analyze patterns, draw diagrams, and think critically

🧩Ratios and Proportions

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
20 Practice Questions
📝 Practice Questions
  • 1 Find the inverse ratio of 1:2:3.
  • 2 If 15% of A is equal to 20% of B, then what is the ratio A:B?
  • 3 An amount of Rs 2250 is divided among Ajay, Vijay and Rahul such that 1/6 of Ajay’s share, 1/4 of Vijay’s share and 2/5 of Rahul’s share are equal. Find Ajay’s share.
  • 4 A sum is divided among A, B, C and D in the ratio 5:2:4:3. If C gets Rs 1000 more than D, find B’s share.
  • 5 Seats for Maths, Physics and Biology are in the ratio 5:7:8. They are increased by 40%, 50% and 75%. Find the new ratio.
  • 6 The ratio of boys to girls is 3:2. If 20% boys and 25% girls scored ≥90%, what percentage scored less than 90%?
  • 7 Rs 160 consists of 1 rupee, 50 paise and 25 paise coins in ratio 4:5:6. Find the number of 25 paise coins.
  • 8 Income ratio of Ajay and Vijay is 3:2 and expenditure ratio is 5:3. If both save Rs 1000, find Ajay’s income.
  • 9 Students in 3 batches are in ratio 2:3:5. After adding 20 students to each, ratio becomes 4:5:7. Find original total students.
  • 10 Divide Rs 500 among P, Q, R and S such that (P+Q) = 3(R+S), Q = 4R and R = 1.5S. Find Q’s share.
  • 11 Income of A is 10% more than B and B is 20% less than C. Find ratio A:B:C.
  • 12 Tickets priced Rs 1000, Rs 500 and Rs 200 are sold in ratio 3:2:5. Total collection is Rs 2.5 crore. Find number of tickets sold.
  • 13 Find three numbers in ratio 1:2:3 such that sum of their squares is 504.
  • 14 Ratio of marks of A and B is 5:7. If 5A = 3B + 12, find their marks.
  • 15 Salary of A is 80% of B and salary of C is 120% of A. Find ratio A:B:C.
  • 16 In 120 litres mixture, milk:water = 2:1. To make it 1:2, how much water should be added?
  • 17 If 0.75 : x :: 5 : 8, find x.
  • 18 Find the fourth proportional to 3, 4, 15.
  • 19 Speeds of three bikes are in ratio 3:5:7. Find ratio of time taken for same distance.
  • 20 Find the mean proportional between 6 and 24.

🧩Permuations and Combinations

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
24 Practice Questions
📝 Practice Questions
  • 1 From a group of 5 men and 6 women, four persons are to be selected to form a committee. In how many ways can this be done?
  • 2 From 5 men and 6 women, select 5 persons such that at least 3 men are included. In how many ways?
  • 3 From 5 men and 6 women, select 5 persons such that at most 3 men are included. In how many ways?
  • 4 From 5 men and 6 women, form a committee of 5 with exactly 2 men and 3 women. In how many ways?
  • 5 A box has 3 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn such that at least one is red?
  • 6 In how many ways can a team of 11 be selected from 15 players such that 2 particular players are always included?
  • 7 In how many ways can a team of 11 be selected from 15 players such that 2 particular players are never together?
  • 8 In how many ways can a team of 11 be formed from 15 players such that one particular player is excluded?
  • 9 There are 8 points on a circle. Find (A) number of lines and (B) number of triangles formed.
  • 10 In how many ways can the letters of the word "LEADING" be arranged?
  • 11 In how many ways can "LEADING" be arranged such that consonants always come together?
  • 12 In how many ways can "ASSASSINATION" be arranged such that vowels always come together?
  • 13 From 5 boys and 3 girls, select 4 such that at least one girl is included. In how many ways?
  • 14 How many 4-digit numbers can be formed using digits 0,1,2,3,4 without repetition and divisible by 5?
  • 15 A box has 3 white, 4 black and 5 red balls. In how many ways can 4 balls be drawn such that at least one is white?
  • 16 In how many ways can "RETAIL" be arranged such that vowels occupy only even positions?
  • 17 How many 4-digit even numbers can be formed using digits 2,3,4,5 without repetition?
  • 18 In how many ways can 5 men and 6 women be seated such that no two men sit together?
  • 19 How many 4-letter words can be formed from "FATHERLY" using each letter once and including a particular letter?
  • 20 How many 4-letter words can be formed from "LINEAR" with repetition allowed but excluding letter A?
  • 21 How many words can be formed using letters of "bbbbcccccddef"?
  • 22 In how many ways can 5 balls be placed in 3 buckets?
  • 23 In how many ways can 10 students be seated in a circle?
  • 24 How many words can be formed from "GRANDMOTHER" such that vowels never come together?
  • 💡 Solve each question independently | No solutions provided

🧩Probability

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
24 Practice Questions
📝 Practice Questions
  • 1 From a group of 5 men and 6 women, four persons are to be selected to form a committee. In how many ways can this be done?
  • 2 From 5 men and 6 women, select 5 persons such that at least 3 men are included. In how many ways?
  • 3 From 5 men and 6 women, select 5 persons such that at most 3 men are included. In how many ways?
  • 4 From 5 men and 6 women, form a committee of 5 with exactly 2 men and 3 women. In how many ways?
  • 5 A box has 3 white, 3 black and 4 red balls. In how many ways can 3 balls be drawn such that at least one is red?
  • 6 In how many ways can a team of 11 be selected from 15 players such that 2 particular players are always included?
  • 7 In how many ways can a team of 11 be selected from 15 players such that 2 particular players are never together?
  • 8 In how many ways can a team of 11 be formed from 15 players such that one particular player is excluded?
  • 9 There are 8 points on a circle. Find (A) number of lines and (B) number of triangles formed.
  • 10 In how many ways can the letters of the word "LEADING" be arranged?
  • 11 In how many ways can "LEADING" be arranged such that consonants always come together?
  • 12 In how many ways can "ASSASSINATION" be arranged such that vowels always come together?
  • 13 From 5 boys and 3 girls, select 4 such that at least one girl is included. In how many ways?
  • 14 How many 4-digit numbers can be formed using digits 0,1,2,3,4 without repetition and divisible by 5?
  • 15 A box has 3 white, 4 black and 5 red balls. In how many ways can 4 balls be drawn such that at least one is white?
  • 16 In how many ways can "RETAIL" be arranged such that vowels occupy only even positions?
  • 17 How many 4-digit even numbers can be formed using digits 2,3,4,5 without repetition?
  • 18 In how many ways can 5 men and 6 women be seated such that no two men sit together?
  • 19 How many 4-letter words can be formed from "FATHERLY" using each letter once and including a particular letter?
  • 20 How many 4-letter words can be formed from "LINEAR" with repetition allowed but excluding letter A?
  • 21 How many words can be formed using letters of "bbbbcccccddef"?
  • 22 In how many ways can 5 balls be placed in 3 buckets?
  • 23 In how many ways can 10 students be seated in a circle?
  • 24 How many words can be formed from "GRANDMOTHER" such that vowels never come together?
  • 💡 Solve each question independently | No solutions provided

🧮 Seating Arrangements

Percentages, profit & loss, ratios, averages, time & work, numbers
6 Practice Questions
📝 Practice Questions
  • 1 A, P, R, X, S and Z are sitting in a row. S and Z are in the centre. A and P are at the ends. R is sitting to the left of A. Who is to the right of P?
  • 2 Five girls are sitting on a bench to be photographed. Seema is to the left of Rani and to the right of Bindu. Mary is to the right of Rani. Reeta is between Rani and Mary. Who is sitting immediate right to Reeta? Who is in the middle of the photograph? Who is second from the right? Who is second from the left in photograph?
  • 3 A gets more marks than B but less than C. D gets less marks than E but more than A. If C gets less than D then who amongst A, B, C, D, E gets the highest marks?
  • 4 Hari and Akash are ranked seventh and eleventh respectively from the top in a class of 31 students. What will be their respective ranks from the bottom in the class?
  • 5 Rajeev ranks seventh from the top and twenty eighth from the bottom in a class. How many students are there in the class?
  • 6 Six friends P, Q, R, S, T and U are sitting around a hexagonal table each at one corner and facing the centre. P is second to the left of U. Q is neighbour of R and S. T is second to the left of S. Which one is sitting opposite to P? Who is the fourth person to the left of Q? Which of the following are the neighbours of P? Which one is sitting opposite to T?

🧮 Set Theory

Percentages, profit & loss, ratios, averages, time & work, numbers
8 Practice Questions
📝 Practice Questions
  • 1 If X and B are two sets, then (X − Y) ∩ Y is ………………….. a. X b. Y c. X ∪ Y d. X ∩ Y e. { }
  • 2 250 people read English newspaper and 350 people read Hindi newspaper. There are 25 people who read both of these newspapers. Find the number of persons who read 1 or 2 of these newspapers.
  • 3 100 students play badminton, 160 students play cricket. There are 25 students who play both of these games. The total number of students in the class is 300. What is: (a) number of students playing at least 1 game? (b) number of students not playing any of the two games? (c) the number of students playing only badminton? (d) the number of students playing only cricket?
  • 4 In a class of 150 students numbered 1 to 150, all even numbered students opt for Biology, those whose numbers are divisible by 5 opt for Chemistry, and those whose numbers are divisible by 7 opt for Physics. How many opt for none of the three subjects?
  • 5 Of the 200 candidates who were interviewed for a position at a company, 80 had bikes, 70 had cars and 120 had cycles. 30 of them had both a bike and a car, 40 had a car and a cycle, 40 had both a bike and a cycle and 10 had all three. How many candidates had none of the three?
  • 6 In a class of 50 students, 20 enrolled for both French and German. 25 enrolled for German. If all students enrolled for at least one of the two subjects, then how many students enrolled for only French and not German?
  • 7 In a class, 45% of the students enrolled for Computers and 65% enrolled for English classes. If 15% of the students enrolled for both Computers and English, what percentage of the students did not enroll for either of the two subjects?
  • 8 In a school, 120 students have English only, 180 have Hindi, and 200 have German. 40 students have both Hindi and English, 40 have both Hindi and German, and 65 have both German and English. There are 20 students who have all three languages. All students take at least one of the three languages. Calculate the following: (1) Total number of students in school (2) Students having only English (3) Students having only Hindi & English (4) Students having exactly 1 language (5) Students having exactly 2 languages (6) Students having at least 1 language (7) Students having at least 2 languages (8) Students having at most 3 languages (9) Students having Hindi & one other language (10) Students having English & one or more other languages.

🧮 Simple Interest and Compound Interest

Percentages, profit & loss, ratios, averages, time & work, numbers
28 Practice Questions
📝 Practice Questions
  • 1 A sum of Rs.10000 is lent out for 2 years at 5% p.a. Find the simple interest. a) 1000 b) 100 c) 1100 d) 1010
  • 2 A sum of Rs.8000 is lent out for 2 years at 6% p.a. Find the amount. a) 8880 b) 8980 c) 8960 d) 8860
  • 3 A sum of Rs.7500 is lent out for 9 months at 6% per annum. Find the simple interest. a) 337.5 b) 345 c) 415.5 d) 325.75
  • 4 A sum of Rs.6300 is lent out for 8 months at 7% per annum. Find the simple interest. a) 294 b) 196 c) 250 d) 177
  • 5 A sum of Rs.1725 is lent out from May 1st to July 12th at 8% per annum. Find the simple interest. a) 23 b) 27.6 c) 29.88 d) 33
  • 6 The simple interest obtained on a sum of Rs.800 in 2 years is Rs.96. Find the rate of interest per annum. a) 6% b) 8% c) 10% d) 12%
  • 7 The amount obtained on a certain sum in 3 years at 12% per annum is Rs.9792. Find the sum. a) 7500 b) 7000 c) 7200 d) 8000
  • 8 A sum of Rs.16800 is divided into 2 parts and lent out. One at 6% p.a. and the other at 8% p.a. After 2 years the total amount is Rs.19000. Find the sum lent at 6%. a) 12200 b) 9900 c) 11500 d) 3600
  • 9 In what time will the simple interest on a certain sum become 0.125 times of the principal at 10% per annum? a) 1.5 years b) 1.25 years c) 2 years d) 1.333 years
  • 10 The simple interest accrued in 2 years on a principal of Rs.24000 is one-eighth of the principal. What is the rate of interest? a) 6.25% b) 6% c) 7.5% d) 12.5%
  • 11 Ramesh took a loan at 6% per annum and it increased every year by 1.5%. If he pays Rs.8190 as interest at the end of 3 years, what is the loan amount? a) 38600 b) 36000 c) 35500 d) 36400
  • 12 Ramesh invested a certain sum at 5% p.a. and another sum at 6% p.a. He gained Rs.1220 as total interest for one year. If the rates were interchanged, he would have earned Rs.20 less. What is the second sum? a) 10000 b) 11000 c) 12000 d) 13000
  • 13 A sum of Rs.2600 is divided into two parts. One part is lent at 10% p.a. for 5 years and the other at 9% p.a. for 6 years. The simple interests are equal. Find the second sum. a) 1250 b) 1350 c) 2300 d) 2100
  • 14 Rs.6500 is divided into two parts such that the interest on one part at 10% p.a. for 5 years is Rs.530 less than that on the second part at 8% p.a. for 5 years. Find the first sum. a) 2300 b) 2500 c) 3200 d) 4100
  • 15 Find the compound interest on Rs.15000 for 2 years at 10% per annum compounded annually. a) 3750 b) 3000 c) 3050 d) 3150
  • 16 Find the compound interest on Rs.15000 for 1 year at 10% p.a. compounded half-yearly. a) 1537.5 b) 1630 c) 1717 d) 1500
  • 17 Find the compound interest on Rs.33000 for 6 months at 12% p.a. compounded quarterly. a) 2130 b) 2008 c) 2009.7 d) 2209.7
  • 18 The compound interest on Rs.15800 for 2 years is Rs.7716.72. Find the rate of interest. a) 11% b) 19% c) 30% d) 22%
  • 19 What is the approximate compound interest on Rs.4890 at 5% p.a. for 3 years? a) 772 b) 867 c) 923 d) 1100
  • 20 The simple interest on Rs.22500 for 4 years is Rs.10800. What is the compound interest for 2 years at the same rate? a) 5680 b) 5724 c) 5484 d) 5980
  • 21 The simple interest on a sum for 8 years at 13% p.a. is Rs.6500. Find the compound interest for 2 years at 8% p.a. a) 960 b) 1077 c) 1050 d) 1040
  • 22 Find the difference between simple interest and compound interest on Rs.7300 at 6% p.a. for 2 years. a) 30 b) 56.78 c) 78 d) 26.28
  • 23 The difference between simple interest and compound interest for 2 years at 5% p.a. is Rs.15. Find the sum. a) 6000 b) 5400 c) 3500 d) 5000
  • 24 A bank offers 10% compound interest p.a. compounded half-yearly. A customer deposits Rs.1900 on Jan 1 and July 1. Find the interest earned in one year. a) 290 b) 291.75 c) 300 d) 310.11
  • 25 There is a 60% increase in a sum in 3 years at simple interest. Find the compound interest on Rs.15000 for 2 years at the same rate. a) 7000 b) 3400 c) 6600 d) 6100
  • 26 The least number of years in which a sum doubles at 20% compound interest is: a) 3 b) 4 c) 5 d) 6
  • 27 A sum doubles in 8 years at compound interest. In how many years will it become 16 times? a) 45 b) 40 c) 36 d) 32
  • 28 A sum doubles in 5 years at simple interest. In how many years will it become 5 times? a) 20 b) 25 c) 30 d) 35

🧮 Syllogisms

Percentages, profit & loss, ratios, averages, time & work, numbers
10 Practice Questions
📝 Practice Questions
  • 1 All cats are dogs. All dogs are wolves. Conclusions: (1) All cats are wolves (2) All wolves are dogs
  • 2 All tables are chairs. Some chairs are mats. Conclusions: (1) Some mats are tables (2) All tables are mats
  • 3 All pens are pencils. All scales are pens. Conclusions: (1) All pencils are scales (2) All scales are pencils
  • 4 All beds are cots. All cots are rugs. Conclusions: (1) All rugs are cots (2) All beds are rugs
  • 5 Some rules are good. All rules are bad. Conclusions: (1) No rule is bad (2) Some rules are bad
  • 6 All cats are dogs. No dogs are wolves. Conclusions: (1) No cats are wolves (2) Some wolves are cats
  • 7 Some guns are bombs. No bomb is bullet. Conclusions: (1) Some bullets are bombs (2) No bullet is gun (3) Some bullets are guns
  • 8 All guns are bombs. Some bombs are not bullets. Conclusions: (1) All guns being bullets is a possibility (2) Some guns are not bullets
  • 9 All red are green. Some green are blue. Conclusions: (1) No red is blue (2) Some red is blue
  • 10 All flowers are bouquets. Some bouquets are thorns. Conclusions: (1) No flower is thorn (2) Some flower is thorn

🧮 Time and Work

Percentages, profit & loss, ratios, averages, time & work, numbers
8 Practice Questions
📝 Practice Questions
  • 1 A can do a work in 15 days and B in 20 days. If they work together for 5 days, then the fraction of work left is: a) 5/12 b) 3/4 c) 6/11 d) 7/9
  • 2 A can construct a road in 16 days and B in 20 days. With the help of C, they completed the job in 8 days. In how many days can C alone do the work? a) 80 b) 65 c) 50 d) 40
  • 3 A, B and C can do a piece of work in 10, 20 and 30 days respectively. In how many days can A complete the work if B and C assist him on every third day? a) 10 b) 11 c) 9 d) 4
  • 4 A can finish a job 60 days earlier than B. Working together, in how many days can they complete the work? a) 20 b) 25 c) 22.5 d) 18
  • 5 A alone can complete a work in 8 days and B in 12 days. They undertake the work for Rs.6000. With the help of C, they finish the work in 4 days. How much should C be paid? a) 500 b) 1000 c) 2500 d) 1100
  • 6 A can do a piece of work in 8 days; B and C together can do it in 4 days, while A and C together can do it in 3 days. In how many days can B alone complete the work? a) 20 b) 24 c) 13 d) 10
  • 7 A can complete a work in the same time as B and C together. If A and B together can do it in 8 days and C alone in 40 days, then in how many days can B alone complete the work? a) 18 b) 19 c) 20 d) 23
  • 8 A completes 80% of a work in 10 days. He then calls B, and together they finish the remaining work in 1 day. In how many days can B alone complete the whole work? a) 7 b) 8.33333 c) 11.11 d) 9.09

🧮 Time Speed and Distance

Percentages, profit & loss, ratios, averages, time & work, numbers
43 Practice Questions
📝 Practice Questions
  • 1 A person crosses an 800 m long street in 10 minutes. What is his speed in km/hr? a) 4.8 b) 5 c) 5.6 d) 7
  • 2 A car covers a distance at 60 kmph in 5 hours. To cover the same distance in 2 hours, what speed is required? a) 150 kmph b) 200 kmph c) 80 kmph d) 100 kmph
  • 3 If a person walks at 18 km/hr instead of 12 km/hr, he would have walked 40 km more. What is the actual distance? a) 50 km b) 35 km c) 80 km d) 100 km
  • 4 A train can travel 100% faster than a car. Both start together and reach 50 km away at the same time, but the train stops for 20 minutes. Find the speed of the train. a) 135 kmph b) 160 kmph c) 150 kmph d) 175 kmph
  • 5 The ratio of speeds of two trains is 4:3. If the second train covers 100 km in 2 hours, what is the speed of the first train? a) 33.33 kmph b) 66.66 kmph c) 75 kmph d) 55 kmph
  • 6 A car travelling at 5/7 of its speed covers 54 km in 1 hr 40 min 48 sec. Find the actual speed. a) 35 kmph b) 45 kmph c) 50 kmph d) 55 kmph
  • 7 A man completes a journey in 10 hours, travelling first half at 20 km/hr and second half at 25 km/hr. Find total distance. a) 222.222 km b) 333.333 km c) 444.444 km d) 555.555 km
  • 8 Abhay takes 3 hours more than Sameer to cover 40 km. If Abhay doubles his speed, he takes 1 hour less than Sameer. Find Abhay’s speed. a) 3 kmph b) 7 kmph c) 8 kmph d) 5 kmph
  • 9 Arjun reaches at 2 PM at 20 kmph and 12 noon at 30 kmph. At what speed should he travel to reach at 1 PM? a) 24 kmph b) 21 kmph c) 25 kmph d) 26.36 kmph
  • 10 A farmer travelled 65 km in 10 hours, partly walking at 5 kmph and partly cycling at 7 kmph. Find distance walked. a) 12 km b) 12.5 km c) 13 km d) 13.5 km
  • 11 A man would take 80 minutes less if he moved 6 kmph faster and 80 minutes more if 4 kmph slower. Find the distance. a) 80 km b) 120 km c) 140 km d) 160 km
  • 12 In a 10 km race, A beats B by 1 km and B beats C by 1 km. By how much does A beat C? a) 2 km b) 2.2 km c) 1.5 km d) 1.9 km
  • 13 In a 100 m race, A gives B 10 m and C 25 m. How much can B give C? a) 6.666 m b) 16.666 m c) 26 m d) 28.91 m
  • 14 In a 100 m race, A runs at 8 kmph and gives B 12 m start, yet beats him by 10 sec. Find B’s speed. a) 4.14 kmph b) 12 kmph c) 5 kmph d) 5.76 kmph
  • 15 In an 800 m race, speeds of A:B = 5:6 and A has 250 m start. By how much does A win? a) 100 m b) 40 m c) 125 m d) 140 m
  • 16 In a 200 m race, A beats B by 36 m or 6 sec. Find A’s time. a) 25 s b) 27.33 s c) 29.99 s d) 30 s
  • 17 A runs 1 1/5 times as fast as B. If A gives B 100 m start, find distance of race. a) 200 m b) 400 m c) 600 m d) 800 m
  • 18 A train at 44 kmph crosses a man in 10 seconds. Find train length. a) 122.22 m b) 140 m c) 155 m d) 211 m
  • 19 A 160 m train passes a man running at 4 kmph in same direction in 10 sec. Find train speed. a) 12 kmph b) 20 kmph c) 25 kmph d) 10 kmph
  • 20 A 100 m train crosses a bridge in 40 sec at 36 kmph. Find bridge length. a) 250 m b) 300 m c) 350 m d) 500 m
  • 21 Two trains at 50 kmph & 40 kmph cross in same direction in 40 sec. Find combined length. a) 111.111 m b) 222.222 m c) 333.333 m d) 444.444 m
  • 22 Two trains at 50 kmph & 40 kmph cross in opposite direction in 40 sec. Find combined length. a) 1 km b) 900 m c) 1.2 km d) 1.333 km
  • 23 A train passes platform in 42 sec and man in 24 sec at 36 kmph. Find platform length. a) 180 m b) 200 m c) 250 m d) 240 m
  • 24 Two trains (1.2 km & 0.8 km) at 50 & 100 kmph opposite. Time to cross? a) 45 s b) 48 s c) 50 s d) 52 s
  • 25 A jogger at 10 kmph is 300 m ahead of a 160 m train at 46 kmph. Time to cross? a) 30 s b) 36 s c) 46 s d) 50 s
  • 26 Two 150 m trains cross in 10 sec, one twice speed of other. Find faster speed. a) 15 m/s b) 20 m/s c) 25 m/s d) 30 m/s
  • 27 Two 400 m trains at 45 & 15 kmph opposite. Time to pass driver? a) 18 s b) 12 s c) 20 s d) 24 s
  • 28 Trains at 60 & 40 kmph same direction. Fast train passes man in 10 sec. Find length. a) 40 m b) 44.444 m c) 50 m d) 55.555 m
  • 29 A train crosses another (half its length) in 12 sec and platform in 45 sec. Find platform length. a) 400 m b) 420 m c) 444.444 m d) 450 m
  • 30 Two trains start at 8 AM & 9 AM from A & B (100 km apart). Speeds 20 & 10 kmph. When meet? a) 10:30 AM b) 11:40 AM c) 12:50 PM d) 1 PM
  • 31 After meeting, trains reach in 9 & 16 hours. Find speed ratio. a) 2:3 b) 3:7 c) 4:3 d) 1:1
  • 32 Boat speed 14 kmph, stream 6 kmph. Time for 80 km downstream? a) 4 hrs b) 6 hrs c) 3 hrs d) 5 hrs
  • 33 Speed with current 16 kmph, current 4 kmph. Speed against current? a) 8 kmph b) 12 kmph c) 10 kmph d) 14 kmph
  • 34 Upstream 8h36m, downstream 3h48m. Find ratio boat:stream. a) 8:3 b) 6:7 c) 23:37 d) 31:12
  • 35 Downstream 14 km in 2h, upstream in 7h. Find still water speed. a) 3.5 kmph b) 4 kmph c) 5 kmph d) 6.5 kmph
  • 36 Boat speed 10 kmph, current 5 kmph. Distance in 24 min downstream? a) 4 km b) 5 km c) 6 km d) 7 km
  • 37 Boat speed 6 kmph, current 2 kmph. Round trip in 2h. Distance? a) 2 km b) 3.333 km c) 4.555 km d) 5.333 km
  • 38 Downstream 1h, upstream 1.5h, current 5 kmph. Find still water speed. a) 20 kmph b) 25 kmph c) 27.77 kmph d) 30 kmph
  • 39 Boatman goes 3 km upstream in 1h and 2 km downstream in 10 min. Time for 10 km still water? a) 1h b) 1h15m c) 1h20m d) 1h33m
  • 40 Boat speed 7 kmph, current 3.5 kmph. Round trip 105 km. Time? a) 40 hrs b) 44 hrs c) 50 hrs d) 57.77 hrs
  • 41 Time upstream is double downstream. Find ratio boat:stream. a) 1:3 b) 3:1 c) 1:4 d) 4:1
  • 42 A rows 50 km and back in 16h. 6 km downstream = 2 km upstream time. Find stream speed. a) 2 kmph b) 3.333 kmph c) 4.166 kmph d) 4.25 kmph
  • 43 Two persons run on 200 m circular track at 5 m/min and 20 m/min. Find: (a) first meeting time (b) meeting at start (c) number of meeting points (d) same for opposite direction.

🧮 Directions

Percentages, profit & loss, ratios, averages, time & work, numbers
10 Practice Questions
📝 Practice Questions
  • 1 A person starts from his home and goes 150 metres towards north. After turning left, he walks 100 metres. Again he turns left and walks 150 metres. In which direction and at what distance is he from his home now?
  • 2 Virat starts from office and walks 40 m towards south. She turns left and walks 50 m, then turns left again and walks 40 m. Finally she turns right and walks 100 m. How far and in what direction is she from the office?
  • 3 Karan starts from his home and walks 40 metres towards east, then takes a right turn and walks 30 metres. What is his distance from the starting point and in which direction is he now?
  • 4 Rani walked 40 m towards north, then turned right and walked 50 m. Then turned right and walked 65 m, then turned left and walked 15 m, and finally turned left and walked 25 m. In which direction and how many metres is he from the starting position?
  • 5 Anjali put his timepiece on the table such that at 6 P.M. the hour hand points to North. In which direction will the minute hand point at 10:45 P.M.?
  • 6 A man is facing South-East. He turns 90° clockwise, then 180° anticlockwise and then another 90° in the same direction. Which direction is he facing now?
  • 7 One morning after sunrise, Sunny was standing facing a pole. The shadow of the pole fell exactly to his left. Which direction was he facing?
  • 8 One morning after sunrise Arun and Nikhil were talking face to face. If Nikhil's shadow was exactly to the right of Arun, which direction was Nikhil facing?
  • 9 Madhu starts cycling in the morning facing the Sun. After some time, he takes a 45° turn to his left and then again turns 90° towards his left. In which direction is he now?
  • 10 If north-west becomes south, north-east becomes west and so on, then south will become which direction?

🧩 Averages

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
21 Practice Questions
📝 Practice Questions
  • 1 Find the average of first 30 natural numbers.
  • 2 The average of 2, 7, 6 and x is 5 and the average of 18, 1, 6, x and y is 10. What is the value of y?
  • 3 The average weight of 15 boys in a class is 40 kg and that of the remaining 10 boys is 50 kg. Find the average weights of all the boys in the class.
  • 4 The average of five consecutive odd numbers is 83. What is the fourth number in the descending order?
  • 5 The average of 4 consecutive even numbers A, B, C and D respectively is 79. What is the product of A and D?
  • 6 The average age of P boys is x years and of q girls is y years. What is the average age of all together?
  • 7 Nine persons went to a hotel for taking their meals. Eight of them spent Rs 12 each and the ninth spent Rs 8 more than the average expenditure of all nine. What was the total money spent by them?
  • 8 In the first 20 overs of a cricket game, the run rate was only 5. What should be the run rate in the remaining 30 overs to reach the target of 295 runs?
  • 9 A museum has an average of 550 visitors on Sundays and 250 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?
  • 10 The average age of a committee of 8 members is 40 years. A member aged 55 years retired and was replaced by another aged 39 years. What is the new average age?
  • 11 The average weight of 8 persons increases by 2.5 kg when a new person replaces one weighing 65 kg. What might be the weight of the new person?
  • 12 The captain of a cricket team of 11 members is 29 years old and the wicket keeper is 26 years old. If their ages are excluded, the average age of remaining players is one year less than the team average. What is the average age of the team?
  • 13 The average of 10 numbers is calculated as 15. One number 36 was wrongly read as 26. What is the correct average?
  • 14 The average age of 40 students is 8 years. Including the teacher increases the average by 0.5 years. What is the age of the teacher?
  • 15 A contractor employs 20 male, 15 female and 5 child workers. Daily wages are Rs 25, Rs 20 and Rs 8 respectively. What is the average wage per day?
  • 16 The average monthly income of a family of four is Rs 10000. After one daughter leaves, the average becomes Rs 9500. What was her income?
  • 17 Average salary of 24 workers is Rs 2800. The supervisor earns Rs 6500. What is the average salary of all 25 employees?
  • 18 The average marks of 9 students is 54. Three scored 80, 56 and 62. What is the average of remaining 6 students?
  • 19 If the average of 11 consecutive odd numbers is 17, what is the difference between the smallest and largest number?
  • 20 Average age of 30 boys is 15. A 21-year-old leaves and a new boy joins. New average is 14.8. What is the age of the new boy?
  • 21 The average weight of 10 men decreases by 1 kg when a 50 kg man is replaced. What is the weight of the new man?

🧩 Mixtures and Alegations

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
15 Practice Questions
📝 Practice Questions
  • 1 In what ratio must a shopkeeper mix two types of rice worth Rs 50 per kg and Rs 70 per kg so that the average cost is Rs 65 per kg?
  • 2 A container has 50 litres of milk. 10 litres are removed and replaced with water. This is repeated once more. How much milk is left now?
  • 3 In what ratio must sugar at Rs 1.15 and Rs 1.24 per kg be mixed so that selling at Rs 1.50 gives 25% gain?
  • 4 How much water should be mixed with 36 litres of milk costing Rs 5 per litre so that the mixture costs Rs 3.60 per litre?
  • 5 How many kg of sugar at 50 paise per kg must be mixed with 25 kg at 34 paise per kg so that selling at 44 paise gives 10% gain?
  • 6 How much sugar at Rs 9.5 per kg should be added to 17 kg of tea at Rs 20 per kg so that the mixture is worth Rs 13 per kg?
  • 7 A hospital mixture costs Rs 7.62 per litre with 5% salt. Another mixture has 75% water and costs Rs 7.82 per litre. What will be the cost of 5 litres mixture containing 18% salt?
  • 8 A vessel has a mixture with 20% spirit. 5 litres are removed and replaced with water. Now spirit is 12%. What is the total quantity of the vessel?
  • 9 An alloy has 65% copper. Another has copper and nickel in ratio 17:3. In what ratio should they be mixed so that copper is 4 times nickel?
  • 10 One mixture has 88% sulphur and another has 70%. In what ratio should they be mixed to get 84% sulphur?
  • 11 In what ratio should water be mixed with juice costing Rs 12 per litre to obtain mixture worth Rs 8 per litre?
  • 12 In what proportion should water be mixed with milk to gain 40% by selling at cost price?
  • 13 A 400 gm solution has 30% spirit. What ratio of spirit should be added to make it 80%?
  • 14 One alloy has silver and copper in ratio 5:1 and another in 7:2. What quantities should be mixed to make 5 lb alloy with 80% silver?
  • 15 Box A has wheat at Rs 30/kg and Box B at Rs 40/kg. Mixed in ratio 4:7, what is the price per kg of the mixture?

🧩Number Series

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
15 Practice Questions
📝 Practice Questions
  • 1 In what ratio must a shopkeeper mix two types of rice worth Rs 50 per kg and Rs 70 per kg so that the average cost is Rs 65 per kg?
  • 2 A container has 50 litres of milk. 10 litres are removed and replaced with water. This is repeated once more. How much milk is left now?
  • 3 In what ratio must sugar at Rs 1.15 and Rs 1.24 per kg be mixed so that selling at Rs 1.50 gives 25% gain?
  • 4 How much water should be mixed with 36 litres of milk costing Rs 5 per litre so that the mixture costs Rs 3.60 per litre?
  • 5 How many kg of sugar at 50 paise per kg must be mixed with 25 kg at 34 paise per kg so that selling at 44 paise gives 10% gain?
  • 6 How much sugar at Rs 9.5 per kg should be added to 17 kg of tea at Rs 20 per kg so that the mixture is worth Rs 13 per kg?
  • 7 A hospital mixture costs Rs 7.62 per litre with 5% salt. Another mixture has 75% water and costs Rs 7.82 per litre. What will be the cost of 5 litres mixture containing 18% salt?
  • 8 A vessel has a mixture with 20% spirit. 5 litres are removed and replaced with water. Now spirit is 12%. What is the total quantity of the vessel?
  • 9 An alloy has 65% copper. Another has copper and nickel in ratio 17:3. In what ratio should they be mixed so that copper is 4 times nickel?
  • 10 One mixture has 88% sulphur and another has 70%. In what ratio should they be mixed to get 84% sulphur?
  • 11 In what ratio should water be mixed with juice costing Rs 12 per litre to obtain mixture worth Rs 8 per litre?
  • 12 In what proportion should water be mixed with milk to gain 40% by selling at cost price?
  • 13 A 400 gm solution has 30% spirit. What ratio of spirit should be added to make it 80%?
  • 14 One alloy has silver and copper in ratio 5:1 and another in 7:2. What quantities should be mixed to make 5 lb alloy with 80% silver?
  • 15 Box A has wheat at Rs 30/kg and Box B at Rs 40/kg. Mixed in ratio 4:7, what is the price per kg of the mixture?

📖 Blood Relations

Synonyms, antonyms, sentence correction, idioms, fill in the blanks
15 Practice Questions
📝 Practice Questions
  • 1 Pointing to a photograph Ramu said, “He is the father of my father’s father’s son”. How is Ramu related to the man in the photograph?
  • 2 Pointing to a boy in the photograph, Rani said, “His sister is the only daughter of my father”. How is the boy related to Rani’s husband?
  • 3 Pointing to Yathish, Sundari said, “He is the husband of my father’s only daughter”. How is Yathish related to Sundari?
  • 4 A girl introduced a boy as the son of the daughter of the father of her uncle. The boy is the girl's?
  • 5 Pointing to a lady, a man said, "The son of her only brother is the brother of my wife." How is the lady related to the man?
  • 6 Manu told Harish, "The girl I met yesterday at the beach was the youngest daughter of the sister-in-law of my friend's father." How is the girl related to Manu's friend?
  • 7 Pointing to a photograph, a man said, "I have no brother or sister but that man’s father is my father’s son." Whose photograph was it?
  • 8 A is brother of B, C is sister of B. How is B related to C?
  • 9 A is the brother of B. B is the brother of C. D is the father of A. Based on these statements, which statement cannot be definitely true?
  • 10 A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?
  • 11 In a family of six members A, B, C, D, E and F: A and B are married, A is male. D is the only son of C, who is A’s brother. E is D’s sister. B is daughter-in-law of F whose husband is dead. How is F related to E?
  • 12 There are six persons A, B, C, D, E and F. C is sister of F. B is brother of E’s husband. D is father of A and grandfather of F. There are two fathers, three brothers and a mother. Who is the mother?
  • 13 A man said, "The lady in the photograph is my nephew's maternal grandmother." How is the lady related to the man's sister (who has no other sister)?
  • 14 If 'A $ B' means 'A is brother of B', 'A @ B' means 'A is wife of B', 'A # B' means 'A is daughter of B' and 'A & B' means 'A is father of B', which expression indicates 'K is father-in-law of H'?
  • 15 A family consists of P, Q, R, X, Y and Z. Q is son of R but R is not mother. P and R are married. Y is brother of R. X is daughter of P. Z is brother of P. Who is the brother-in-law of R?

🧩Partnership

Blood relations, direction sense, coding-decoding, puzzles, series, syllogisms
13 Practice Questions
📝 Practice Questions
  • 1 Raj invested Rs 76000 in a business. After a few months Monty joined with Rs 57000. At the end of the year profits are shared in the ratio 2:1. After how many months did Monty join?
  • 2 A and B started a business in the ratio 5:6. C joined after 6 months with an amount equal to B. Total profit is Rs 102000. How much did C invest?
  • 3 Sita and Geeta invested Rs 120000 and Rs 135000 respectively. Find their shares in a profit of Rs 35700.
  • 4 Ravi invested Rs 36000. After 3 months Shyam joined with Rs 36000. Find their shares in a profit of Rs 37100.
  • 5 Sony, Mony and Tony invested Rs 20000 each. After 5 months Sony withdrew Rs 5000, Mony withdrew Rs 4000 and Tony added Rs 6000. Total profit is Rs 69900. Find their shares.
  • 6 Sheela invested Rs 21000. Reema joined later with Rs 36000. After how many months did Reema join if profits are equal?
  • 7 X and Y share profits in the ratio 2:3. If X invested Rs 40000, find the investment of Y.
  • 8 Mohinder and Surinder invested Rs 12000 and Rs 9000. After 3 months Sudhir joined with Rs 15000. Find Sudhir's share in a half-year profit of Rs 9500.
  • 9 In a partnership, A invests 1/6 capital for 1/6 time, B invests 1/3 capital for 1/3 time and C invests the rest for full time. Find B’s share in Rs 4600.
  • 10 Ajay and Sahil invested Rs 50000 and Rs 40000 respectively and share profit in that ratio. Find Ajay’s share in Rs 22500.
  • 11 Navdeep invested Rs 16000 for 9 months, Rahul Rs 12000 for 6 months and Raj Rs 8000 for 12 months. Total profit is Rs 26000. Find Rahul’s share.
  • 12 Divya invested Rs 3500. After 5 months Jyoti joined. Profit ratio is 2:3. How much did Jyoti invest?
  • 13 Aman invested Rs 550 and Rahul Rs 330. Profit ratio is 10:3. After how many months did Rahul join?

📊 Calenders

Tables, bar graphs, pie charts, line graphs, caselets
10 Practice Questions
📝 Practice Questions
  • 1 What was the day on 15th August 1947?
  • 2 What was the day on 10th December 2001?
  • 3 If today is Monday, after 63 days it will be?
  • 4 If today is Thursday, after 51 days it will be?
  • 5 The last day of a century cannot be?
  • 6 How many leap years does 100 years have?
  • 7 On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
  • 8 The calendar for the year 1993 will repeat again in which year?
  • 9 If Aug 21st, 2012 falls on Thursday then March 11th, 2013 falls on which day?
  • 10 The calendar of the year 2024 can be used again in which year?

🎲 Clocks

Arrangements, combinations, probability basics, counting principles
15 Practice Questions
📝 Practice Questions
  • 1 What is the time shown on the mirror of an unnumbered clock if the actual time is 3:45?
  • 2 The number of times the minute and the hour hand form 90 degrees between 1 pm and 4 pm is?
  • 3 The number of times the minute and the hour hand form 180 degrees between 4 pm and 8 pm is?
  • 4 How many times will a broken clock show the correct time in 4 days?
  • 5 At what time between 4 pm and 5 pm will the hour and the minute hand form an angle of 90 degrees?
  • 6 At what time between 4 pm and 5 pm will the hour and the minute hand form an angle of 180 degrees?
  • 7 At what time between 4 pm and 5 pm will the hour and the minute hand form a straight line?
  • 8 What is the angle formed between the hour hand and the minute hand if they are 30 minutes apart?
  • 9 What is the angle formed between the hour and the minute hand at 8:45 pm?
  • 10 What is the angle formed between the hour and the minute hand at 2:25 pm?
  • 11 A clock started at noon. The hour hand has turned by how many degrees at 8:30 pm?
  • 12 Jeevan sets his clock right at 3 pm on Monday. The clock gains 60 seconds every hour. What is the time shown at 6:30 pm on Wednesday?
  • 13 A clock was set right at 10 am on Monday. If the clock loses 10 minutes every hour then when will it show the correct time?
  • 14 A watch which gains uniformly is 5 minutes slow at 8 o'clock in the morning on Sunday and 5 minutes 48 seconds fast at 8 pm on the following Sunday. When was it correct?
  • 15 A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day?

⏱️ Coding and Decoding

Work efficiency, pipes & cisterns, speed-distance-time, trains
10 Practice Questions
📝 Practice Questions
  • 1 In a certain code ‘CAT’ is written as ECV. How is ‘DOG’ written in that code?
  • 2 If the word VIKAS is written as 22911119, how will you write the word VISHWAS?
  • 3 If PUNCH = 62, then KICK = ?
  • 4 If HISTORY is coded as IHTSPQZ, then GEOGRAPHY is coded as?
  • 5 If JERRI is coded as NVUGK, then CID is coded as?
  • 6 If POKEMON is coded as KLPVNLM, then DORAEMON is coded as?
  • 7 If Red is called Blue, Blue is called Yellow, Yellow is called White, White is called Pink and Pink is called Black, then what is the colour of the sky?
  • 8 In a certain code language, '134' means 'good and tasty'; '478' means 'see good pictures' and '729' means 'pictures are faint'. Which digit stands for 'see'?
  • 9 In a certain code language, ‘sit na dom’ means ‘bring me water’, ‘na ko tod’ means ‘water is life’, ‘tub od sit’ means 'give me toy’ and ‘ko lin kot’ means ‘life and death’. Which word represents 'is'?
  • 10 If Red means Blue, Blue means Yellow, Yellow means White, White means Pink and Pink means Black, then what is the colour of the sky?