Time and Work Questions

Multiple choice
  1. 10:11

  2. 11:10

  3. 20:21

  4. 21:20

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

Q's rate: 1 task / (25 * 12) = 1/300 per hour. R's rate: 1 task / (50 * 12) = 1/600 per hour. Q worked 5 days * 12 hours = 60 hours. Work Q = 60/300 = 1/5. R worked 7 days * 18 hours = 126 hours. Work R = 126/600 = 21/100. Ratio Q:R = 1/5 : 21/100 = 20/100 : 21/100 = 20:21.

Multiple choice
  1. 10 days

  2. 20 days

  3. 15 days

  4. 30 days

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

X's daily work is 1/30. Y and Z's combined daily work is 1/45 + 1/90 = 3/90 = 1/30. On day 1, X works alone (1/30). On day 2, X, Y, and Z work together (1/30 + 1/30 = 2/30 = 1/15). In a 2-day cycle, they complete 1/30 + 2/30 = 3/30 = 1/10 of the work. Thus, it takes 10 cycles of 2 days each, totaling 20 days.

Multiple choice
  1. 11 : 9

  2. 11 : 3

  3. 7 : 9

  4. 9 : 11

  5. NA

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

Let rates be A+B=1/20, B+C=1/50, A+C=1/40. Summing gives 2(A+B+C) = 1/20 + 1/50 + 1/40 = (10+4+5)/200 = 19/200. So A+B+C = 19/400. A = 19/400 - 1/50 = 11/400. B = 19/400 - 1/40 = 9/400. Ratio of time taken (inverse of rates) is 9:11.