Time and Work Questions

Multiple choice
  1. 14

  2. 61/3

  3. 23/3

  4. 60/7

  5. 10

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

A, B, and C work at rates of 1/12, 1/36, and 1/48 per day. In 2 days, they complete 2*(1/12 + 1/36 + 1/48) = 2*(12+4+3)/144 = 19/72. Then A and C work for 3 days, completing 3*(1/12 + 1/48) = 3*(5/48) = 15/48 = 5/16. The remaining work is 1 - (19/72 + 5/16) = 1 - (38+45)/144 = 1 - 83/144 = 61/144. C completes this at a rate of 1/48, taking (61/144) * 48 = 61/3 days.

Multiple choice
  1. 8 days

  2. 9 days

  3. 11 days

  4. 14 days

  5. 16 days

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

B takes 20 days, A takes 30 days. Work rates: B=1/20, A=1/30. Together: 1/20+1/30 = 5/60 = 1/12. In 6 days, they do 6/12 = 1/2 work. Remaining 1/2. B does half of remaining (1/4) in 5 days. Remaining 1/4. A+B do 1/4 at rate 1/12 in 3 days. Total = 6+5+3 = 14 days.

Multiple choice
  1. 72

  2. 90

  3. 12

  4. 68

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

A's rate is 1/20, B's is 1/30. A works for 4 days, doing 4/20 = 1/5 of the work. Remaining work is 4/5. B and C complete this in 18 days, so (1/30 + C) * 18 = 4/5. Solving for C: 1/30 + C = 4/90 = 2/45. C = 2/45 - 1/30 = 4/90 - 3/90 = 1/90. Thus, C takes 90 days.