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

Saurabh and Tarun can complete a piece of work in 36 days and 48 days repectively for which they get ₹28,800. But with the help of Pawan they will complete the whole work in 12 day then how much amount Pawan will get ? सौरभ और तरुण किसी कार्य को 36 व 48 दिनो मे पूर्ण कर सकते है एवं उन्हे इस कार्य को पूर्ण करने के लिए 28800 रू प्राप्त होते है। परन्तु वे पवन की सहायता से इस कार्य को 12 दिनो मे पूर्ण करे तो पवन को कितनी धनराशि प्राप्त होगी ?

  1. 1000

  2. 1200

  3. 12000

  4. 14400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Saurabh's work rate: 1/36 per day. Tarun's work rate: 1/48 per day. Combined (Saurabh + Tarun + Pawan) rate: 1/12 per day. Pawan's rate = 1/12 - (1/36 + 1/48) = 1/12 - 7/144 = 12/144 - 7/144 = 5/144. Ratio of work rates: Saurabh : Tarun : Pawan = 4/144 : 3/144 : 5/144 = 4:3:5. Total parts = 12, Pawan's share = 5/12 of ₹28,800 = ₹12,000.

Multiple choice

Naimish take twice as much time as Arun and thrice as much as Deepak. If they all work together and finish the work in 2 days . Find in how many days Deepak can alone finish the work? नैमिष अरुण से दुगना समय और दीपक से तीन गुना समय लेता हैं कार्य पूरा करने में | यदि ये तीनो एक साथ कार्य करें तो कार्य 2 दिन में समाप्त हो जाता हैं |ज्ञात कीजिये दीपक अकेले ये कार्य कितने दिनों में पूरा केर सकता हैं ?

  1. 6

  2. 4

  3. 12

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

Let Naimish, Arun, and Deepak take n, a, and d days respectively. Given n = 2a and n = 3d, so their one-day work is 1/n, 1/a, 1/d. Working together: (1/n + 1/a + 1/d) = 1/2. Since n = 3d, Arun takes 1.5d days. Combined rate: 1/(3d) + 1/(1.5d) + 1/d = 1/(3d) + 2/(3d) + 1/d = 2/d. Therefore 2/d = 1/2, giving d = 4 days for Deepak alone.

Multiple choice

A takes half time as B to do a work. C takes time equal to A and B together. If three together can do the work in 7 days then in how many days A alone can do the work? A एक काम को करने में B से आधा समय लेता है। C काम करने में, A और B के एक साथ काम करने में लगे समय के बराबर समय लेता है। यदि तीनों एक साथ काम करे 7 दिन में करते है, तो A अकेला कितने समय में काम करेगा?

  1. 14 days / दिन

  2. 21 days / दिन

  3. 28 days / दिन

  4. 18 days / दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B's time be 2x, so A's time is x. A's rate = 1/x, B's rate = 1/(2x). C's time = A + B together = x + 2x over their combined rate. Combined rate of A and B = 1/x + 1/(2x) = 3/(2x), so C's time = 1 ÷ (3/(2x)) = 2x/3. C's rate = 1/(2x/3) = 3/(2x). Together: 1/x + 1/(2x) + 3/(2x) = 3/x = 1/7, so x = 21. A alone takes 21 days.

Multiple choice

Ram is four times as efficient as Shyam. If both can complete the work in 11 days then in how many days Shyam will complete the work? राम, श्याम से चार गुना दक्ष है। यदि दोनों मिलकर एक काम को 11 दिनों में पूरा करें तो श्याम अकेले उस काम को कितने दिनों में पूरा करेगा?

  1. 44 days / दिन

  2. 55 days / दिनों

  3. 60 days / दिनों

  4. 33 days / दिनों
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ram's efficiency = 4 × Shyam's. If Shyam does x work/day, Ram does 4x work/day. Together: 5x work/day. Work completed in 11 days: 11(5x) = 55x = total work. Shyam alone: 55x/x = 55 days. If Ram worked alone: 55x/(4x) = 13.75 days. 44 days would be if Ram was 5 times efficient, 33 days if equal efficiency.

Multiple choice

A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. then how many number of men in orignal? कुछ आदमी एक कार्य को 60 दिन में पूरा करते है। यदि 8 आदमी और हो तो कार्य 10 दिन कम में पूरा हो सकता है। तो प्रारंभ में आदमियों की संख्या कितनी थी ?

  1. 32

  2. 36

  3. 30

  4. 40
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let m be the original number of men. Work = m × 60 man-days. With (m+8) men: (m+8) × 50 = m × 60. Solving: 50m + 400 = 60m, so 10m = 400, giving m = 40 men. Verification: 40 × 60 = 2400 man-days, and 48 × 50 = 2400 man-days. Both calculations match.

Multiple choice

A contractor undertake to finish a certain work in 124 days and employed 120 men. After 64 days, he found that he had already done 2/3 of the work. How many men can be discharged so that the work may finish in time ? एक ठेकेदार ने 124 दिनों में किसी काम को पूरा करने का ठेका लिया। उसने 120 व्यक्ति कार्य पर लगाये परन्तु 64 दिन में 2 /3 कार्य ही हो पाया तो कितने व्यक्ति को हटाया जाये की कार्य समय पर समाप्त हो जाये?

  1. 50

  2. 48

  3. 56

  4. 64
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work done in 64 days by 120 men = 120 × 64 = 7680 man-days, which equals 2/3 of total work. Total work = 7680 × 3/2 = 11520 man-days. Remaining work = 11520 - 7680 = 3840 man-days. Remaining time = 124 - 64 = 60 days. Men needed = 3840/60 = 64. Men discharged = 120 - 64 = 56.

Multiple choice

Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and the ratio of their wages as 5 : 3 : 2. When 90 men are employed , total daily wages of all Rs 10350. find the daily wages of a woman . आदमी औरत और बच्चे 3 : 2 : 1 के समानुपात में कार्य करने के लिए लगाये जाते है और इनकी मजदूरी का अनुपात क्रमश 5 : 3 : 2 है यदि 90 आदमी कार्यरत है तो सभी लोगों की कुल दैनिक मजदूरी 10350 रु. है तो एक औरत की दैनिक मजदूरी ज्ञात कीजिये |

  1. 75

  2. 45

  3. CND/ निर्धारित नही किया जा सकता है

  4. 115
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Number of women = 90 × (2/3) = 60, children = 90 × (1/3) = 30. Let wages be 5x, 3x, 2x. Total = 90(5x) + 60(3x) + 30(2x) = 690x = 10350, so x = 15. Woman's wage = 3x = 45.

Multiple choice

A and B together can complete a work in 3 days.They started together but after 2 days. B left the work .If the work is completed after 2 more days, in how many days could B alone do the same work? A और B एक काम को 3 दिनों में कर सकते है। वे एक साथ काम करना प्रारम्भ करते है, लेकिन 2 दिन बाद B काम छोड़ देता है यदि काम 2 दिन बाद पूरा होता है तो B अकेला काम को कितने दिनों में पूरा कर सकता है?

  1. 5

  2. 6

  3. 7

  4. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A + B do 1/3 work per day. After 2 days, 1/3 work remains, done by A alone in 2 days, so A's rate = 1/6 per day. B's rate = (1/3 - 1/6) = 1/6, so B alone takes 6 days.

Multiple choice

A piece of work can be done by 6 men and 5 women in 6 days or it can be done by 3 men and 4 women in 10 days.Find in how many days it can be done by 9 men and 15 women ? एक काम को 6 आदमी और 5 औरत 6 दिन में पूरा करते है ,जबकि यही काम 3 आदमी और 4 औरत 10 दिन में पूरा करते है । उसी काम को 9 आदमी और 15 औरतें कितने दिन में पूरा करेगी?

  1. 5 days/ दिन

  2. 3 days/ दिन

  3. 4 days/ दिन

  4. 4.5 days/ दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let 1 man's 1 day work = m, 1 woman's 1 day work = w. From given: 6m + 5w = 1/6 (work per day), and 3m + 4w = 1/10. Solving: Multiply second eq by 2: 6m + 8w = 1/5. Subtract from first: -3w = 1/6 - 1/5 = -1/30, so w = 1/90. Then 6m = 1/6 - 5/90 = 15/90 - 5/90 = 10/90, so m = 1/54. For 9 men + 15 women: daily work = 9/54 + 15/90 = 1/6 + 1/6 = 1/3. Days needed = 1/(1/3) = 3. Answer B is correct.

Multiple choice

A and B can finish a work in 30 days, B and C can finish it in 15 days while C and A can finish it in 10 days. Time taken by them together to do this work is- A और B किसी कार्य को 30 दिन में समाप्त कर सकते हैं, B और C इसे 15 दिन में जबकि C और A इसको 10 दिन में समाप्त कर सकते हैं । इस कार्य को उनको एक साथ पूरा करने में लिया गया समय है -

  1. 15 days/दिन

  2. 10 days/दिन

  3. 18 days/दिन

  4. 20 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work = LCM(30,15,10) = 30 units. Combined rates: A+B = 1 unit/day, B+C = 2 units/day, C+A = 3 units/day. Adding all three: 2(A+B+C) = 6, so A+B+C = 3 units/day. Time together = 30/3 = 10 days.

Multiple choice

2 men and 1 woman can complete a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a man gets Rs.225 per day, what should be the wages per day of a woman?

  1. Rs.105

  2. Rs.150

  3. Rs.25

  4. Rs.185

  5. Rs.125
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Setting up the equations: (2m + w) × 14 = (2m + 4w) × 8, where m and w represent one day's work by a man and woman respectively. Solving gives 12m = 18w, or m/w = 3/2. Since wages should be proportional to efficiency and a man earns Rs.225, a woman should earn 225 × (2/3) = Rs.150 per day.

Multiple choice

3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together at the same rate as before, to finish the same job is-

  1. 20

  2. 30

  3. 36

  4. 40

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

Setting up the equations: 5(3m + 7w) = 4(4m + 6w) = 1. Solving gives 11w = m. Substituting back: 5(40w) = 1, so w = 1/200 of the job per day. For 10 women: 10w = 10/200 = 1/20 of the job per day. Therefore, 10 women take 20 days.

Multiple choice

(2\text{ Men or } 5\text{ Women can complete a work in 16 days. In how many days can }2\text{ Men and }5\text{ Women complete the same work.})

  1. 3

  2. 4

  3. 5

  4. 8

  5. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When 'OR' is used in work-time problems, it means the work rates are equal. Here, 2 Men and 5 Women both complete the work in 16 days, so they have equal rates. Therefore, 2 Men + 5 Women working together equals 4 Men working. If 2 Men take 16 days, then 4 Men (double the workforce) take half the time: 16/2 = 8 days.

Multiple choice

8 men can do a work in 12 days. 4 women can do the same work in 48 days and 10 children can do the same work in 24 days. In how many days will 10 men, 4 women and 10 children do the same work?

  1. 5

  2. 15

  3. 28

  4. 6

  5. 16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Calculate individual rates: 8 men do in 12 days, so 1 man's rate = 1/(8×12) = 1/96 work per day. 4 women do in 48 days, so 1 woman's rate = 1/(4×48) = 1/192 work per day. 10 children do in 24 days, so 1 child's rate = 1/(10×24) = 1/240 work per day. Combined rate of 10M + 4W + 10C = 10/96 + 4/192 + 10/240 = 10/96 + 2/96 + 4/96 = 16/96 = 1/6. Therefore, they complete the work in 6 days.