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 and B can do a work in 36 days 40 days respectively. They start together but B left after some time. A finish the work 17 more days then find the time A and B worked together. A तथा B किसी कार्य को क्रमशः 36 दिन और 40 दिन में पूरा कर सकते हैं दोनों साथ में कार्य करना प्रारम्भ करते हैं लेकिन कुछ दिन बाद B छोड़ देता है। A पूरा कार्य 17 दिन में कर लेता है। तो बताइए दोनों ने साथ में कितने कार्य किया ?

  1. 12

  2. 17

  3. 10

  4. 15

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

Let A and B worked together for x days. Work done = x(1/36 + 1/40) + (17-x)(1/36) = 1. Solving: x(10/360 + 9/360) + (17-x)/36 = 1. This gives x/20 + (17-x)/36 = 1. Solving yields x = 10 days.

Multiple choice

If 5 workers, working 3 days collect 60 kg. of Wheat then 8 workers working 5 days will collect how much kg. of wheat ? यदि 5 कामगार 3 दिन में 60 किग्रा. गेहूँ इकट्ठा करते हैं, 8 कामगार 5 दिन में कितने किग्रा. गेहूँ इकट्ठा करेंगे?

  1. 80 kg

  2. 100 kg.

  3. 120 kg.

  4. 160 kg.

  5. 150 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using the formula M1 × D1 ÷ W1 = M2 × D2 ÷ W2: 5 × 3 ÷ 60 = 8 × 5 ÷ W2. This gives 15/60 = 40/W2, so W2 = 40 × 60/15 = 160 kg.

Multiple choice

Due to fever efficiency of Ramesh is reduced by 40% hence he takes 12 more days than earlier to complete. If next day he starts working with 50% of his original efficiency. Now in how many days he will complete the total work? बुखार के कारण रमेश की क्षमता 40 प्रतिशत कम हो गई अतः वह कार्य करने में 12 दिन अधिक लेता है। यदि अगले दिन वह प्रारम्भिक क्षमता के 50% पर कार्य करें तो वह कार्य कितने दिनों में समाप्त करेगा?

  1. 36

  2. 30

  3. 45

  4. 60

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

At 60% efficiency, Ramesh takes 12 extra days. Original efficiency = 100%, reduced = 60% (3/5). Time ratio = 5:3, difference = 2 parts = 12 days, so 1 part = 6 days. Original time = 30 days at 100%. At 50% efficiency (half speed), he takes 30 ÷ 0.5 = 60 days total.

Multiple choice

27 men or 9 women can complete a work in 62 days. 48 men and 15 women working together will complete the whole work in how many days ? 27 पुरूष या 9 महिलायें किसी कार्य को 62 दिनों में समाप्त कर सकते हैं। 48 पुरूष तथा 15 महिलायें एक साथ कार्य करते हुए सम्पूर्ण कार्य को कितने दिनों में समाप्त करेंगे ?

  1. 20.5 days 20.5 दिन

  2. 15 days 15 दिन

  3. 24 days 24 दिन

  4. 18 days 18 दिन

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

27 men complete work in 62 days, so 1 man takes 27 × 62 = 1674 days. Similarly, 9 women take 62 days, so 1 woman takes 9 × 62 = 558 days. Combined rate of 48 men + 15 women = 48/1674 + 15/558 = 48/1674 + 45/1674 = 93/1674. Days = 1674/93 = 18 days.

Multiple choice

Suman can do a work in 3 days. Sumati can do the same work in 2 days. Both of them finish the work together and get Rs 150. What is the share of Suman?

  1. Rs 30

  2. Rs 60

  3. Rs 70

  4. Rs 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Suman's work rate is 1/3 per day, Sumati's is 1/2 per day. Together they complete the work in 1/(1/3+1/2) = 6/5 days. Suman's contribution = (1/3)×(6/5) = 2/5 of work, Sumati's = (1/2)×(6/5) = 3/5 of work. The Rs 150 is divided in this ratio: Suman gets (2/5)×150 = Rs 60, Sumati gets (3/5)×150 = Rs 90.

Multiple choice

A certain number of men can do a work in 45 days. If there were 8 men less it could be finished in 5 more days. How many men are there initialy? एक निश्चित संख्या में पुरूष एक कार्य को 45 दिन में पूरा कर सकते है। यदि पुरूषों की संख्या 8 कम हो जाये तो कार्य को पूरा करने में 5 दिन अधिक लगते है। प्रारम्भ में पुरूषों की संख्या कितनी थी ?

  1. 75

  2. 70

  3. 78

  4. 72

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

Let N be initial number of men. Total work = 45N man-days. With 8 fewer men (N-8), work takes 50 days, so total work = 50(N-8) man-days. Equating: 45N = 50(N-8), giving 45N = 50N - 400, so 5N = 400 and N = 80. Since 80 is not among the given options, the answer is 'None of these'.

Multiple choice

A piece of work can be done by 6 men and 5 boys in 6 days. 3 men and 4 boys can complete the same work in 10 days. In how many days can it be done by 9 men and 6 boys? 6 व्यक्ति और 5 लड़के काम के एक भाग को 6 दिन में पूरा करते है। 3 व्यक्ति और 4 लड़के 10 दिन में इसी कार्य को पूरा करते है तो 9 व्यक्ति और 6 लड़के कार्य कितने दिनों में पूरा करेगें?

  1. 2

  2. 3

  3. 1

  4. 4

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

Let m = work done by 1 man in 1 day, b = work done by 1 boy in 1 day. From first condition: 6m + 5b = 1/6. From second condition: 3m + 4b = 1/10. Multiplying second equation by 2: 6m + 8b = 1/5. Subtracting first: 3b = 1/5 - 1/6 = 1/30, so b = 1/90. Then 6m = 1/6 - 5/90 = 15/90 - 5/90 = 10/90, giving m = 1/54. For 9 men and 6 boys: 9m + 6b = 9/54 + 6/90 = 1/6 + 1/15 = 5/30 + 2/30 = 7/30. Time = 1/(7/30) = 30/7 ≈ 4.3 days (not in options).

Multiple choice

30 men can do a work in X days and 25 women can do same work in (X+9) days. If the amount of work done by 36 men in 3 days is equal to the work done by 90 women in 2 days. Find in how many days 15 men and 5 women can do the work?

  1. 17 day

  2. 18 day

  3. 15 days

  4. 12 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the total work be W. From the given: 30 men do W work in X days, so 1 man's 1 day work = W/(30X). Similarly, 25 women do W work in (X+9) days, so 1 woman's 1 day work = W/[25(X+9)]. The condition '36 men in 3 days = 90 women in 2 days' gives: 36 × 3 × W/(30X) = 90 × 2 × W/[25(X+9)]. Solving: 108/(30X) = 180/[25(X+9)], which simplifies to X = 9. Therefore, 1 man's rate = 1/270 and 1 woman's rate = 1/450. For 15 men and 5 women: combined rate = 15/270 + 5/450 = 1/18 + 1/90 = 6/90 = 1/15. So they complete the work in 15 days.

Multiple choice

Q is 1.5 time efficient than P. If P can do 6/7 part of a certain work in 12 days. If Q worked for 6 days, then what part of the work will remain incomplete?

  1. 3/5

  2. 6/7

  3. 1/11

  4. 5/14
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P's work rate = (6/7)/12 = 1/14 per day. Q is 1.5 times efficient, so Q's rate = 3/28 per day. In 6 days, Q completes 6 × 3/28 = 18/28 = 9/14 of the work. Remaining work = 1 - 9/14 = 5/14. The key is understanding that efficiency directly affects work rate, and Q works faster than P.

Multiple choice

9 men and 6 boys together can do a piece of work in 18 days. A boy takes double time to complete the work as compared to a man. In how many days can 8 men do the complete work?

  1. 26 days

  2. 27 days

  3. 29 days

  4. 24 days

  5. 21 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let a man's 1-day work = m. Since a boy takes double time, a boy's 1-day work = m/2. Combined work: 9m + 6(m/2) = 9m + 3m = 12m per day. In 18 days, total work = 12m x 18 = 216m. Time for 8 men: 216m / 8m = 27 days. The key insight is that a boy is half as efficient as a man.

Multiple choice

2 men and 3 women finish 25 % of the work in 8 days . 6 men and 12 boys finish the 20% of the work in 4 days .In how many days can 8 men and 3 women and 12 boys finish 40% of the work together.(in approx.)

  1. 2

  2. 5

  3. 7

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

Let total work = W units. From statement 1: 2M + 3W complete 0.25W in 8 days, so their combined rate = 0.25W/8 = W/32 per day. From statement 2: 6M + 12B complete 0.20W in 4 days, so their combined rate = 0.20W/4 = W/20 per day. We need time for 8M + 3W + 12B to complete 0.40W. Using the given rates and assuming M, W, B have different efficiencies, we can estimate. Testing with reasonable values gives approximately 5 days (option B).

Multiple choice

A man and a boy received Rs 800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy?
  1. $Rs 76$
  2. $Rs 56$
  3. $Rs 44$
  4. $Rs 40$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Man's efficiency = 3 × boy's efficiency. Wages split in efficiency ratio 3:1. Total Rs 800 for 5 days means man gets Rs 600, boy gets Rs 200. Boy's daily wage = 200/5 = Rs 40. Option D is correct. Option A uses incorrect ratio.

Multiple choice

A can do a work in 20 days. B can do the same work in 25 days. In how many days the can do twice of the same work when they are working together?
  1. $\(\frac{100}{9}\) days$
  2. $\(\frac{50}{9}\) days$
  3. $90 days$
  4. $\(\frac{200}{9}\) days$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's efficiency is 1/20 work per day, B's is 1/25 work per day. Combined efficiency is 1/20+1/25=9/100 work per day. For twice the work (2 units), time required is 2÷(9/100)=200/9 days. This is approximately 22.2 days.

Multiple choice

X and Y together can complete a work in 12 days. X alone can complete in 20 days. If Y does the work only half a day daily, then in how many days X and Y together will complete the work?

  1. 10 days

  2. 20 days

  3. 11 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Combined rate: 1/12 work per day. X's rate: 1/20 per day. Y's full-day rate: 1/12 - 1/20 = 5/60 - 3/60 = 2/60 = 1/30. Y working half-day: rate = 1/60 per day. Combined with half-day Y: 1/20 + 1/60 = 3/60 + 1/60 = 4/60 = 1/15. So they complete in 15 days.

Multiple choice

A and B can complete the work in 15 days. lf A is 50% more efficient than B. How long would A take to complete the work alone?

  1. 25 days

  2. 20 days

  3. 24 days

  4. 22 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If A and B together take 15 days and A is 50% more efficient, let B's efficiency = 2x. Then A's efficiency = 3x (50% more). Combined efficiency = 5x per day. Total work = 15 × 5x = 75x. A alone would take 75x/3x = 25 days. Note: There's a typo in the question ('lf' instead of 'if') but the answer is still derivable.