Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

A B and C can do a piece of work in 50, 75 and 20 days respectively. They all work together for 4 days, then C left the work.Then find out in how many days A and B take to finish the rest of the work?

  1. 20

  2. 30

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 4 days, A does 4/50, B does 4/75, C does 4/20 = 1/5. Total done = 4/50 + 4/75 + 4/20 = 12/150 + 8/150 + 30/150 = 50/150 = 1/3. Work remaining = 2/3. A+B's combined rate = 1/50 + 1/75 = 5/150 = 1/30. Time needed = (2/3) / (1/30) = 20 days.

Multiple choice

A work can be completed by P and Q in 12 and 16 days respectively. With the help of R they can complete the work in 6 days and earned Rs. 3696. Then find the share of R.

  1. 924

  2. 693

  3. 231

  4. 462
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P completes work in 12 days, so rate = 1/12 per day. Q completes in 16 days, so rate = 1/16 per day. Together with R, they complete in 6 days. Combined rate = 1/6 per day. R's rate = 1/6 - 1/12 - 1/16 = (8 - 4 - 3)/48 = 1/48 per day. Earnings of Rs. 3696 are divided in ratio of their rates: (1/12) : (1/16) : (1/48) = 4 : 3 : 1. R's share = 3696 × 1/8 = 462.

Multiple choice

Three person P,Q and R are assigned for a work. P and Q together can do it in 40 days, Q and R can do it in 36 days and all three together can do that work in 24 days. Then find in how many days Q alone can do the same work?

  1. 60

  2. 90

  3. 72

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P, Q, R be work rates per day. P + Q = 1/40, Q + R = 1/36, P + Q + R = 1/24. Subtracting first from third: R = 1/24 - 1/40 = 1/60. Then Q = 1/36 - 1/60 = 1/90. So Q alone takes 90 days. Options A, C, D are common miscalculations from incorrect subtraction.

Multiple choice

Puneet hires three person X, Y and Z to do a piece of work. They can do the piece of work in 50, 75 and 20 days respectively. They started working together after 4 days Z quits the work. In how many days X and Y take to finish the rest of the work ?

  1. 20

  2. 30

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X, Y, Z complete work in 50, 75, 20 days respectively. Their combined rate = 1/50 + 1/75 + 1/20 = 3/150 + 2/150 + 7.5/150 = 12.5/150 per day. In 4 days, they complete 50/150 = 1/3 of work. Remaining work = 2/3. X + Y rate = 1/50 + 1/75 = 5/150 per day. Time for remaining work = (2/3) / (5/150) = 100/5 = 20 days. Options B, C, D are calculation errors.

Multiple choice

A can do 25% of the work in 8 days, B can 1/8th of the work in 12 days. In how many days they can do 75% of the job by working together?

  1. 24

  2. 9

  3. 21

  4. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A does 25% (1/4) work in 8 days, so A's rate = 1/32 per day. B does 1/8 work in 12 days, so B's rate = 1/96 per day. Combined rate = 1/32 + 1/96 = 4/96 = 1/24 per day. For full work: 24 days. For 75% (3/4) of work: 3/4 × 24 = 18 days. Options A, B, C are incorrect conversions between percentages and fractions.

Multiple choice

The ratio of efficiency of A, B and C is 7: 5: 8, together they can complete a work in 42 days. B and C worked together for 21 days and A did the remaining work alone, then find how long it took to complete the work (in days )? A, B और C की दक्षता का अनुपात 7: 5: 8 है, एक साथ मिलकर वे किसी काम को 42 दिनों में पूरा कर सकते हैं| B और C ने 21 दिनों तक एक साथ कार्य किया और शेष कार्य A ने अकेले पूरा किया तो ज्ञात कीजिए कार्य पूरा होने में कितना समय लगा (दिनों में)?

  1. 102

  2. 81

  3. 87

  4. 75

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total efficiency = 7+5+8 = 20 units/day. Total work = 20×42 = 840 units. B+C efficiency = 13 units/day. In 21 days, B+C complete 21×13 = 273 units. Remaining = 840-273 = 567 units. A does 567/7 = 81 days alone. Total time = 21 + 81 = 102 days.

Multiple choice

A can complete a piece of work in 12 days, A, B and C can complete the work in 6 days. Efficiency of B is 0.5 times the efficiency of A. In how many days C can complete the work alone? A काम को 12 दिनों में पूरा कर सकता है, A, B और C 6 दिनों में काम पूरा कर सकते हैं। B की दक्षता A की दक्षता का 0.5 गुना है। C अकेले कितने दिनों में कार्य पूरा कर सकता है?

  1. 10 days

  2. 16 days

  3. 24 days

  4. 12 days

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/12. A+B+C rate = 1/6. B's efficiency = 0.5 × A, so B's rate = 0.5/12 = 1/24. C's rate = (1/6) - (1/12 + 1/24) = (4/24 - 2/24 - 1/24) = 1/24. So C alone takes 24 days. Option C is correct.

Multiple choice

36 Men completes a work in 24 days working 8 hour daily. 48 women completes same work in 20 days working 10 hours daily. 14 men and 25 women together working 12 hours/day will complete total work in how many days? 36 आदमी किसी कार्य को को रोजाना 8 घण्टे काम करके 24 दिनों में पूरा करते हैं। 48 औरतें उसी कार्य को रोजाना 10 घण्टे कार्य करके 20 दिनों में पूरा करती हैं। 14 आदमी तथा 25 औरतें पूरे कार्य को कितने दिनों में पूरा करेंगी। यदि वे रोजाना 12 घण्टे कार्य करें ।

  1. 18

  2. 16

  3. 20

  4. 16.5

  5. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Men: 36 men × 24 days × 8 hours = 6912 man-hours. One man-hour = Work/6912. Women: 48 women × 20 days × 10 hours = 9600 man-hours. One woman-hour = Work/9600. Combined work in one 12-hour day: (14 men × 12 × Work/6912) + (25 women × 12 × Work/9600) = (168/6912 + 300/9600) × Work = (0.0243 + 0.03125) × Work = 0.05556 × Work. Days needed = Work/(0.05556 × Work) = 18 days.

Multiple choice

8 males and 6 females can do a piece of work in 5 days. 5 males and 6 females can complete the same work in 7 days. How many days will a female take to do the job, if she works alone? 8 पुरुष और 6 महिलाएं 5 दिनों में एक काम कर सकते हैं। 5 पुरुष और 6 महिला एक ही काम को 7 दिनों में पूरा कर सकते हैं। एक महिला को काम करने में कितने दिन लगेंगे, अगर वह अकेली काम करती है ?

  1. 135 days 135 दिन

  2. 142 days 142 दिन

  3. 126 days 126 दिन

  4. 110 days 110 दिन

  5. None of these इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let one male's one day work = m and one female's one day work = f. From first condition: 8m + 6f = 1/5. From second condition: 5m + 6f = 1/7. Subtract second equation from first: 3m = 1/5 - 1/7 = 2/35, so m = 2/105. Substitute in second equation: 5(2/105) + 6f = 1/7, so 10/105 + 6f = 1/7, giving 6f = 15/105 - 10/105 = 5/105 = 1/21. Therefore f = 1/126. One female alone will take 126 days to complete the work.

Multiple choice

The following question has some statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. In how many days 14 men can complete a piece of work? Statement 1: If 18 women can complete the same piece of work in 24 days. Statement 2: If 28 children can complete the same piece of work in 56 days.

  1. Only 1

  2. Only 2

  3. Both 1 and 2

  4. Neither 1 or 2

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Neither statement provides information about men's work rate or any conversion between men, women, and children. Without knowing how men's work compares to women or children, or any relationship between these groups, we cannot determine how long 14 men would take.

Multiple choice

In how many days will 6 men complete a work? Statement 1: 6 men and women can complete the work in 12 days. Statement 2: 8 men can complete the work in 16 days.

  1. Only 1

  2. Only 2

  3. Both 1 and 2

  4. either 1 or 2

  5. Neither 1 or 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement 1 alone is insufficient because we don't know how many women are working with the 6 men. Statement 2 alone is sufficient: if 8 men complete the work in 16 days, then 6 men will take (8×16)÷6 = 64/3 days using the inverse proportion between workers and time.

Multiple choice

A, B and C together can complete a piece of work in 20 days. The working efficiency of A, B and C is in the ratio of 3 : 4 : 5. Then find in how many days the total work can be completed by faster person ? A, B और C मिलकर 20 दिनों में एक काम पूरा कर सकते हैं। A, B और C की कार्य क्षमता 3: 4: 5. के अनुपात में है। तो बताइए की तेज गति वाला आदमी अकेले पूरा कार्य कितने दिन में पूरा कर सकता है ?

  1. 40 days

  2. 48 days

  3. 36 days

  4. 72 days

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let efficiencies be 3x, 4x, 5x. Combined efficiency = 12x. Combined work = 12x × 20 = 240x. C is fastest (5x), so C alone needs 240x ÷ 5x = 48 days. The 'faster person' refers to the most efficient worker, C.

Multiple choice

If A can do ¼ of a work in 6 days and B can do 1/6 of the same work in 8 days, how much will A get if both work together and are paid Rs 360 in all? यदि A किसी कार्य के 1/4 भाग को 6 दिनों में कर सकता है और B उसी कार्य के 1/6 भाग को 8 दिनों में कर सकता है, तो A को कितनी राशि मिलेगा यदि दोनों एक साथ काम करते हैं और कुल 360 रुपये का भुगतान किया जाता है?

  1. 120

  2. 72

  3. 150

  4. 140

  5. None of these इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

A's rate: (1/4 work) in 6 days, so full work in 24 days. Rate = 1/24 per day. B's rate: (1/6 work) in 8 days, so full work in 48 days. Rate = 1/48 per day. Combined rate = 1/24 + 1/48 = 3/48 = 1/16 per day. They finish in 16 days. A's contribution = 16 days × (1/24) = 16/24 = 2/3 of work. A's share = (2/3) × 360 = Rs 240. Since 240 is not among options A-D, 'None of these' (E) is correct.