X can complete one work in 5 days. Y can complete the same work twice in 15…
2020
X can complete one work in 5 days. Y can complete the same work twice in 15 days, and Z can complete the same work three times in 7 days. If they work together for 8 hours a day, how much time will they take to complete one work?
- A.
10 hrs 15 minute
- B.
9 hrs 45 minute
- C.
10 hrs 30 minute
- D.
11 hrs 15 minute
Attempted by 4 students.
Show answer & explanation
Correct answer: C
CONCEPT: In time-and-work questions, each person's capacity is converted into a rate: work completed per day. When people work together, their rates are added; if a workday has fixed hours, fractional working days are converted into hours by multiplying by hours per day.
X completes 1 work in 5 days, so X's rate is 1/5 work per day.
Y completes 2 works in 15 days, so Y's rate is 2/15 work per day.
Z completes 3 works in 7 days, so Z's rate is 3/7 work per day.
Combined rate = 1/5 + 2/15 + 3/7 = 21/105 + 14/105 + 45/105 = 80/105 = 16/21 work per day.
Time for 1 work = 1 divided by (16/21) = 21/16 working days.
Each working day is 8 hours, so time = (21/16) × 8 = 21/2 hours = 10.5 hours.
CROSS-CHECK: In 10.5 working hours, the fraction of an 8-hour day is 10.5/8 = 21/16 days; multiplying this by the combined rate 16/21 gives exactly 1 full work.
Therefore, the required time is 10 hours 30 minutes.