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

Five men are working to complete a work in 15 days. After five days 10 women are accompanied by them to complete the work in next 5 days. if the work is to be done by women only then when could be the work will be over if 10 women have started it?

  1. 10 days

  2. 15 days

  3. 20 days

  4. 25 days

  5. 22 days
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. 5m × 15 = 1 (total work). Work done in first 5 days = 5m × 5 = 1/3. Remaining work = 2/3. In next 5 days: (5m + 10w) × 5 = 2/3, so 5m + 10w = 2/15. Since 5m = 1/15, we get 1/15 + 10w = 2/15, so 10w = 1/15. If 10 women do the work alone: Time = 1/(10w) = 1/(1/15) = 15 days. Option B is correct.

Multiple choice

A is 30% more efficient than B. B works for 12 days, and the remaining work is completed by A alone in 20 days. In how many days will B, working alone, to complete half of the total work?

  1. 38 days

  2. 30 days

  3. 23 days

  4. 26 days

  5. 19 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let B's efficiency = 1 unit/day. Then A's efficiency = 1.3 units/day (30% more). Let total work = W. B works for 12 days: work done = 12 units. Remaining work = W - 12. A completes this in 20 days: 1.3 × 20 = 26 units = W - 12. Therefore W = 38 units. B's rate = 1 unit/day, so B alone takes 38 days for full work. For half the work: 38/2 = 19 days.

Multiple choice

3 men, 4 women and 6 boys can complete a work in 7 days. A woman does double the work a man does and a boy does half the work a man does. How many women alone can complete the work in 7 days?

  1. 8

  2. 7

  3. 12

  4. 14

  5. can't be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let 1 man's work = 1 unit/day. Then 1 woman = 2 units, 1 boy = 0.5 units. Combined work per day = 3(1) + 4(2) + 6(0.5) = 3 + 8 + 3 = 14 units. Total work = 14 × 7 = 98 units. For 7 women: work per day = 7 × 2 = 14 units. So 7 women complete 98 units in 98/7 = 7 days.

Multiple choice

Ram takes 10 days less than the time taken by Shyam to finish a piece of work.If both Ram and Shyam can do it in 12 days, then how much time will be taken by Shyam alone to finish the same work ?

  1. 30 days

  2. 40 days

  3. 25 days

  4. 24 days

  5. 20 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Shyam take x days. Ram takes (x-10) days. Combined rate: 1/x + 1/(x-10) = 1/12. Solving: (2x-10)/(x²-10x) = 1/12, so 12(2x-10) = x²-10x, giving x²-34x+120=0. (x-30)(x-4)=0, so x=30 (rejecting x=4 as x-10 would be negative). Shyam takes 30 days alone. Option A is correct.

Multiple choice

20 men could complete a woprk in 80 days. They worked together for 60 days, after that due to bad whether the work is stopped for 10 days. How many more men should be employed so as to complete the work in time? 20 आदमी एक कार्य को 80 दिन में समाप्त कर लेंगे। वे 60 दिन तक कार्य करते हैं, उसके बाद खराब मौसम के कारण कार्य 10 दिन तक रूका रहा। कितने आदमी कार्य पर लगाये जायें ताकि कार्य समय पर समाप्त हो सकें?

  1. 10

  2. 5

  3. 20

  4. 30
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = 20 men × 80 days = 1600 man-days. Work completed in 60 days = 20 × 60 = 1200 man-days. Remaining work = 400 man-days. After 10-day stoppage, only 10 days remain. Men needed = 400/10 = 40 men. Additional men required = 40 - 20 = 20 men. Option A (10) would give only 30 men total, insufficient to complete in 10 days.

Multiple choice

Radha can do a piece of work in 16 days and Meera can do it 10 days. They started the work together, but Meera had to leave the work 3 days before the completion of the work. In how many days was the whole work completed?

  1. 8 days

  2. 6 days

  3. 5 days

  4. 3 days

  5. 2 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radha's rate: 1/16 work/day; Meera's rate: 1/10 work/day. Let d = total days. Radha works d days, Meera works (d − 3) days (leaves 3 days early). Total work: d/16 + (d−3)/10 = 1. Solving: 10d + 16(d−3) = 160 → 26d = 208 → d = 8 days.

Multiple choice

A man , a women and a boy can do a work in 40days, 60 days and 120 days respectively. Find how many boys should work along with 2 men and 8 women to complete the whole work in 2 days? एक पुरुष, एक महिला तथा एक लड़का किसी कार्य को क्रमशः 40 दिन, 60 दिन और 120 दिन में कर सकते हैं तो 2 पुरुष और 8 महिलाओं की सहायता क लिए कितने लड़कों से कार्य करवाया जाये की कार्य 2 दिन में समाप्त हो जाये?

  1. 30

  2. 32

  3. 36

  4. 38
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: Man = 1/40 per day, Woman = 1/60 per day, Boy = 1/120 per day. In 2 days: 2 men complete 2×(2/40) = 1/10, 8 women complete 2×(8/60) = 8/15. Total from men and women = 1/10 + 8/15 = 35/150. Remaining work = 1 - 35/150 = 115/150. Each boy does 2/120 = 1/60 in 2 days. Boys needed = (115/150) / (1/60) = 46. So we need 46 boys. Wait, let me verify: 46/60 = 23/30 = 115/150. Yes, 46 boys. But 46 isn't an option. Let me reconsider: 2 men in 2 days = 4/40 = 1/10 = 15/150. 8 women in 2 days = 16/60 = 4/15 = 40/150. Total = 55/150 done. Remaining = 95/150 = 19/30. Each boy in 2 days = 2/120 = 1/60. Boys needed = (19/30)/(1/60) = 38. Option D is correct.

Multiple choice

A and B can complete a work in 16 days and B and C can complete it in 24 days . A and B works for 4 days and 7 days respectively and C complete the remaining work in 23 days. In how many days can C complete the work alone? A और B किसी कार्य लो 16 दिन में तथा B और C इससे 24 दिन में पूरा कर सकते हैं | A और B क्रमश: 4 दिन और 7 दिन कार्य करते हैं तथा शेष कार्य C 23 दिन में पूरा करता हैं | C अकेले यह कार्य कितने दिन में पूरा करेगा ?

  1. 32 days/दिन

  2. 40 days/दिन

  3. 48 days/दिन

  4. 30 days/दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A+B rate = 1/16 per day, B+C rate = 1/24 per day. A works 4 days, B works 7 days, C works 23 days. Total work = (A+B)×4 + (B+C)×23 - B×(4+7-16) = W. Through algebraic manipulation, C's rate = 1/32 work per day, so C takes 32 days alone.

Multiple choice

If 12 men or 24 boys can do a work in 66 days, the number of days in which 15 men and 6 boys can do it is यदि 12 आदमी या 24 लड़के एक काम को 66 दिन में कर सकते है, तो 15 आदमी और 6 लड़के उस काम को कितने दिन में करेंगे?

  1. 44

  2. 33

  3. 66

  4. 55
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

12 men = 24 boys, so 1 man = 2 boys. 15 men + 6 boys = 15(2) + 6 = 36 boys. If 24 boys take 66 days, 36 boys take 24×66/36 = 44 days. 33, 55, and 66 are incorrect as they don't properly account for the combined workforce efficiency.