Time and Work Questions

Multiple choice
  1. Rs. 1500

  2. Rs. 2750

  3. Rs. 2500

  4. Rs. 2000

  5. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work rates: A = 1/15, B = 1/12. Together (A+B) = (4+5)/60 = 9/60 = 3/20. With boy (A+B+Boy) = 1/5 = 4/20. Boy's rate = 4/20 - 3/20 = 1/20. Ratio of work: A:B:Boy = 1/15 : 1/12 : 1/20 = 4:5:3. Total parts = 12. Boy's share = (3/12) * 6000 = 1500.

Multiple choice
  1. 7 5/13 days

  2. 9 4/7 days

  3. 6 3/22 days

  4. 8 6/17 days

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P rate = 1/18. Q rate = 1.2 * (1/18) = 1/15. Combined rate = 1/18 + 1/15 = (5+6)/90 = 11/90. Time for full work = 90/11. Time for 3/4 work = (3/4) * (90/11) = 270/44 = 135/22 = 6 3/22 days.

Multiple choice
  1. 9 11/15 days

  2. 7 17/19 days

  3. 11 3/7 days

  4. 12 5/6 days

  5. None of these

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

Let M and W be the work done by one man and one woman per day. 10(7M + 9W) = 15(5M + 5W) => 70M + 90W = 75M + 75W => 5M = 15W => M = 3W. Total work = 10(7(3W) + 9W) = 10(30W) = 300W. 10M + 8W = 10(3W) + 8W = 38W. Time = 300W / 38W = 150/19 = 7 17/19 days.

Multiple choice
  1. 24 days

  2. 28 days

  3. 32 days

  4. 20 days

  5. None of these

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

P, Q, R complete work in 20 days. Q and R complete 2/5 of work in 14 days, so they complete the whole work in 14 * 5/2 = 35 days. P's rate = 1/20 - 1/35 = (7-4)/140 = 3/140. P works for x days, so x * 3/140 = 3/5 (remaining work). x = (3/5) * (140/3) = 28.

Multiple choice
  1. 10 men

  2. 9 men

  3. 8 men

  4. 6 men

  5. None of these

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work is 20 men * 16 days = 320 man-days. After 5 days, 20 * 5 = 100 man-days are done, leaving 220 man-days. If x men remain, x * (55/3) = 220, so x = 12. Since 20 - 12 = 8 men left, the answer is 8.

Multiple choice
  1. Rs. 850

  2. Rs. 1000

  3. Rs. 600

  4. Rs. 700

  5. None of these

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

A's rate = 1/12, B's rate = 1/16. A+B+C rate = 1 / (16/3) = 3/16. C's rate = 3/16 - 1/12 - 1/16 = 2/16 - 1/12 = 1/8 - 1/12 = (3-2)/24 = 1/24. Share is proportional to work done. C's work = (1/24) / (3/16) = (1/24)*(16/3) = 2/9. Share = 4500 * 2/9 = 1000.

Multiple choice
  1. 2 4/5 days

  2. 4 ½ days

  3. 3 ¾ days

  4. 5 1/3 days

  5. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 1/10 work/day, B does 1/15 work/day. Let x be the days they worked together. (1/10 + 1/15) * x + (1/15) * 8 = 1. (3/30 + 2/30) * x + 8/15 = 1 => 5/30 * x = 7/15 => 1/6 * x = 7/15 => x = 42/15 = 14/5 = 2.8 days.