Time and Work Questions

Multiple choice
  1. $3$ days
  2. $4$ days
  3. $4.5$ days
  4. None

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

A's total work time = 7 * 9 = 63 hours. B's total work time = 6 * 7 = 42 hours. Combined rate = 1/63 + 1/42 = (2+3)/126 = 5/126 work per hour. Working 42/5 hours a day, daily work = (5/126) * (42/5) = 1/3 of the work per day. Total days = 3.

Multiple choice
  1. $12$ days
  2. $13$ days
  3. $13\dfrac{2}{7}$ days
  4. None of these

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

A's rate is 1/16, B's is 1/12. In 2 days, they complete 1/16 + 1/12 = 7/48. In 12 days (6 cycles), they complete 6 * (7/48) = 42/48 = 7/8. Remaining work is 1/8. On day 13, A works and completes 1/16. Remaining is 1/8 - 1/16 = 1/16. On day 14, B completes it in (1/16) / (1/12) = 3/4 days. Total time = 13.75 days.

Multiple choice
  1. Man: $160$ days. Boy : $190$ days
  2. Man: $140$ days. Boy : $280$ days
  3. Man: $240$ days. Boy : $150 $days
  4. Man: $260$ days. Boy : $200$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be man's rate, B be boy's rate. 8M + 12B = 1/10; 6M + 8B = 1/14. Solving this system: 24M + 36B = 3/10; 24M + 32B = 4/14 = 2/7. Subtracting: 4B = 3/10 - 2/7 = (21-20)/70 = 1/70. B = 1/280. 6M + 8(1/280) = 1/14 => 6M + 1/35 = 1/14 => 6M = 5/70 - 2/70 = 3/70. M = 1/140. Times are 140 and 280.

Multiple choice
  1. $5$ days
  2. $\dfrac{11}{2}$ days
  3. $6$ days
  4. $8$  days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate is 1/18 work/day and B's rate is 1/15 work/day. B worked for 10 days, completing 10/15 = 2/3 of the work. The remaining 1/3 of the work is completed by A in (1/3) / (1/18) = 6 days.