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

12 men alone can complete a piece of work in 6 days. Where as 10 men and 21 women together take 3 days to complete the same piece of work. In how many days can 12 women alone complete the piece of work? 12 आदमी एक काम को अकेले 6 दिनों में कर सकते हैं जबकि 10 आदमी और 21 औरतें मिलकर इस काम को 3 दिनों में कर सकते हैं। कितने दिनों में 12 औरतें अकेले इस काम को कर सकती है?

  1. 10

  2. 9

  3. 11

  4. 8
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

12 men complete work in 6 days, so 12×6 = 72 man-days are needed. 10 men + 21 women take 3 days: (10 men + 21 women) × 3 = 72 man-days equivalent. Let 1 woman's work = w. Then 10 men = 72/3 = 24 man-days per 3 days, so 10 men contribute 10×(man's work)×3. Men's rate = 72/12 = 6 work units/day, so each man = 0.5 units/day. Total work in 3 days by 10M+21W: 10×0.5×3 + 21w×3 = 72. Solving gives w = 1/3. Then 12 women's time: 12×(1/3)×t = 72, so t = 9 days.

Multiple choice

10 men can complete a work in 7 days and 10 children take 14 days to complete the work. How many days 5 men and 10 children will take to complete the work? 10 आदमी एक काम को 7 दिनों में पूरा कर सकते हैं और 10 बच्चे काम को 14 दिनों में पूरा कर सकते हैं। 5 आदमी और 10 बच्चे काम को पूरा करने में कितने दिन लेंगे?

  1. 5

  2. 7

  3. 3

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

Work rate: 10 men = 1/7 work per day, 10 children = 1/14 work per day. So 1 child = 1/2 man. 5 men + 10 children = 5 + 5 = 10 men. 10 men complete work in 7 days, so answer is 7 days.

Multiple choice

A, B and C can do a piece of work in 20, 30 and 60 days respectively. How many days does it require to complete the work if A does the work and he is assisted by B and C on every third day? A, B और C क्रमशः 20, 30 और 60 दिनों में एक काम को कर सकते हैं। काम को पूरा करने के लिए कितने दिन की आवश्यकता है यदि A कार्य करता है और उसे हर तीसरे दिन B और C द्वारा सहायता दी जाती है?

  1. 10

  2. 14

  3. 15

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's efficiency = 1/20, B's = 1/30, C's = 1/60. In 3-day cycle: Day 1: A does 1/20, Day 2: A does 1/20, Day 3: A+B+C do 1/20+1/30+1/60 = 6/60. Total in 3 days = 8/60. In 15 days (5 cycles): 5 × 8/60 = 40/60 = 2/3. On day 15: A works, adding 1/20. Cumulative: 2/3 + 1/20 = 47/60. Work completed.

Multiple choice

A can do a piece of work in 16 days and B in 24 days. They take the help of C and three together finish the work in 6 days. If the total renumeration for the work is Rs. 400. The amount (in Rs.) each will receive, in proportion, to do the work is :

  1. A : 150, B : 100, C : 150

  2. A : 100, B : 150, C : 150

  3. A : 150, B : 150, C : 100

  4. A : 100, B : 150, C : 100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate is 1/16, B's is 1/24. Together with C, their combined rate is 1/6, so C's rate = 1/16. The work ratio A:B:C is 1/16:1/24:1/16 = 3:2:3. In Rs. 400, A gets 150, B gets 100, C gets 150.

Multiple choice

Amit and Bhanu takes same time to finish a work as that of Chirag. Bhanu takes 5 days less than Amit and 4 days more than that of Chirag. Amit and Bhanu working on alternate days will complete the whole work in how many days?

  1. 12

  2. 10

  3. 15

  4. 18

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

Let Amit's time = a days, Bhanu = b days, Chirag = c days. Given b = a - 5, b = c + 4, and a + b = 2c. Solving: a = 18, b = 13, c = 9. Total work = LCM(18,13,9) = 234. Amit's rate = 13/day, Bhanu's = 18/day. Alternate days starting with Amit: Day 1-2 = 31 units, repeating 7.5 times gives 248 units in 9 days.

Multiple choice

P and Q together can do a piece of work in 4 days. If P does twice as much work as Q in a given time, find how long P alone would take to do the work? P और Q किसी काम को एक साथ 4 दिनों में करते है। यदि दिये समय में P, Q से दो गुना काम करे तो P अकेले उस काम को कितने समय में करेगा?

  1. 6 days/दिन

  2. 12 days/दिन

  3. 8 days/दिन

  4. 9 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P and Q together complete work in 4 days, so their combined rate is 1/4 of the work per day. Since P does twice as much work as Q in the same time, let Q's rate be x and P's rate be 2x. Then 3x = 1/4, meaning x = 1/12. Therefore P's rate is 2/12 = 1/6 of the work per day, so P alone takes 6 days. The key insight is that work rates add up when people work together.

Multiple choice

Either 8 men or 17 women can paint a house in 33 days. The number of days required to paint three such houses by 12 men and 24 women working at the same rate is: 8 पुरूष या 17 महिलाएं एक घर को 33 दिन में पेंट कर सकते हैं। 12 पुरूषों और 24 महिलाओं द्वारा ऐसे तीन घरों को उसी दर से पेंट करने के लिए अपेक्षित दिनों की संख्या है :

  1. 44

  2. 43

  3. 34

  4. 66
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

8 men or 17 women can paint 1 house in 33 days. So 1 man's rate = 1/(8×33) houses/day, 1 woman's rate = 1/(17×33) houses/day. Combined rate of 12 men and 24 women = 12/(264) + 24/(561) = 1/22 + 1/23.33 ≈ 1/11.16 houses/day. For 3 houses: Days = 3/(1/11.16) ≈ 33.48 ≈ 34 days.

Multiple choice

Find the values and state the correct relationship.\nIt takes ( (X-2) ) men to do a work in ( 2Y ) days and it takes ( (X+6) ) men to do the same work in ( Y ) days.\n\textbf{Quantity I:} ( X )\n\textbf{Quantity II:} ( Y )

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Work is constant, so (men × days) is constant. Therefore: (X-2)(2Y) = (X+6)(Y). Solving: 2XY - 4Y = XY + 6Y, so XY - 10Y = 0, giving Y(X - 10) = 0. Since Y cannot be 0, X = 10. Substituting back: (8)(2Y) = (16)(Y) gives 16Y = 16Y, which is satisfied for any positive Y. Thus X = 10 but Y cannot be uniquely determined, so the relationship cannot be established.

Multiple choice

12 men and 16 women together can complete a work in 26 days while 10 women and 18 children together can complete the work in 20 days. Also, 8 men and 16 children can complete the work in 25 days. 1 man, 1 woman and 1 child start the work and from 2nd day onwards every day 1 new man, 1 new woman and 1 new child join the work. On which day the work shall be completed?

  1. 20th day

  2. 21st day

  3. 22nd day

  4. None of the above

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m, w, c be daily work of 1 man, 1 woman, 1 child. From given: 12m + 16w = 1/26, 10w + 18c = 1/20, 8m + 16c = 1/25. Solving this system and finding m + w + c, then using the pattern of work (n(n+1)/2 × (m+w+c) = 1), we get n = 21.

Multiple choice

P, Q and R can complete a work in (a, b, c) days respectively where (a) is 20 less than (b), (c) is 50% more than (b). P starts the work and leaves after 12 days then Q completes the remaining work in 16 days. Find the time in which R can complete the work.

  1. 20

  2. 40

  3. 60

  4. 50

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

Given a=b-20, c=1.5b. Work equation: 12(1/a) + 16(1/b) = 1. Substituting a=b-20: 12/(b-20) + 16/b = 1. Solving: (12b + 16b - 320)/[b(b-20)] = 1, giving b² - 48b + 640 = 0, so (b-16)(b-40) = 0. b=40 (b≠16 since a would be negative). So c = 1.5×40 = 60 days. R alone takes 60 days.

Multiple choice

In how many days 6 men and 5 women can complete the work working together? Statement I: The ratio of efficiency of man to woman is 2:1 Statement II: 9 Women can complete three-five of the work in 15 days. Statement III: 6 Men and a child together can complete 1/4th work in 12 days while 6 women and the child together can complete two-third of the work in 16 days.

  1. None of these

  2. All statements together are sufficient

  3. Any two are sufficient

  4. I and II or III

  5. All statements together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Statement II: 9 women do 3/5 work in 15 days, so 9 women do 1/5 work in 5 days, meaning 9 women complete work in 25 days. With Statement I giving efficiency ratio 2:1, we can find man and woman rates. Combined rate of 6 men and 5 women can be calculated. Statement III introduces a child and creates alternative solution paths. Either pair (I+II) or (II+III) is sufficient.

Multiple choice

Which information is/are necessary to answer the questions asked? Two persons A and B have work efficiency in the ratio 1: 2 respectively. In how many days can A finish a work alone? I- A and C can together complete a work in 24 days and B and C together can complete 80% of the work in 12 days. II- If B increases his efficiency by 20% then B can finish 20% less work as done by A.

  1. I alone

  2. I or II

  3. I and II together are not sufficient

  4. II alone

  5. I and II together
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A and B have efficiency ratio 1:2. Let A's rate = a, B's rate = 2a. Statement I: A + C together take 24 days, so their combined rate is 1/24. B + C together complete 80% in 12 days, so their combined rate is 0.8/12 = 1/15. We have: a + c = 1/24 and 2a + c = 1/15. Subtracting: a = 1/15 - 1/24 = (8-5)/120 = 3/120 = 1/40. So A takes 40 days alone. Statement I alone is sufficient. Statement II: If B's efficiency increases by 20%, new rate is 2.4a. B finishes 20% less work than A. This doesn't give us absolute values or time to complete specific work. Not sufficient.

Multiple choice

The daily wages of Ramesh and Santosh are Rs.350 and Rs.250. When Ramesh finishes a certain work, he gets a total wage of Rs.6300. When Santosh does the same work, he gets a total wage of Rs.7500. If both of them do it together what is the cost of the work. रमेश और संतोष की दैनिक मजदूरी 350 रु. और 250 रु. है । जब रमेश काम को समाप्त कर लेता है तो उसे कुल मजदूरी के रूप में 6300 रु. मिलते हैं । जब संतोष उसी काम को करता है तो मजदूरी के रूप में 7500 रु. मिलते हैं । यदि दोनों एकसाथ मिलकर वही काम करें तो काम की लागत क्या आएगी ?

  1. Rs. 6750

  2. Rs. 2750

  3. Rs. 6050

  4. Rs. 7050
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ramesh takes 18 days (6300/350), Santosh takes 30 days (7500/250). Their combined rate = 1/18 + 1/30 = 4/45 work per day. Total cost = (350+250) × 45/4 = 6750.

Multiple choice

A is thrice as efficient as B and B is twice as efficient as C, if A, B and C work together how long would they take to complete a job that B takes 10 days to complete? A, B से तिगुना अधिक कार्यकुशल है और B, C से दुगुना कार्यकुशल है, यदि A, B और C एक साथ काम करके कितने दिनों में पूरा करेंगे जबकि B, 10 दिनों में पूरा करता है -

  1. 20/9 days/दिन

  2. 11/9 days/दिन

  3. 3 days/दिन

  4. 4 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Efficiency A:B:C = 6:2:1. B's rate = 1/10. Combined rate = 6/20 + 2/20 + 1/20 = 9/20 job per day. Time = 20/9 days.

Multiple choice

Find the value of both quantities and state the correct relationship.\newline Quantity I: Days in which B can complete work alone, if A and B can complete work in 40 days, B and C in 20 days and C and A in 30 days.\newline Quantity II: Days in which B can complete work alone, if A and B can complete work in 24 days and A is 50% more efficient than B.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: From (A+B) = 1/40, (B+C) = 1/20, (C+A) = 1/30. Adding all: 2(A+B+C) = 1/40 + 1/20 + 1/30 = 13/120. So A+B+C = 13/240. B's rate = (A+B+C) - (A+C) = 13/240 - 1/30 = 3/240 = 1/80. B alone takes 80 days. Quantity II: A+B = 1/24 and A is 50% more efficient than B, so A = 1.5B. Then 2.5B = 1/24, B = 1/60. B alone takes 60 days. Since 60 < 80, Quantity II (smaller days) represents faster completion, so B's capacity is higher.