A, B, and C can do a piece of work in the ratio of their efficiencies 4 : 6 :…
2019
A, B, and C can do a piece of work in the ratio of their efficiencies 4 : 6 : 9. Working together, they complete the work in 72 hours. In how many hours can C alone complete 50% of the work?
- A.
114
- B.
57
- C.
95
- D.
76
Attempted by 47 students.
Show answer & explanation
Correct answer: D
Let the efficiencies of A, B, and C be 4x, 6x, and 9x respectively.
Total combined efficiency = 4x + 6x + 9x = 19x.
They finish the work together in 72 hours, so total work = 72 × 19x = 1368x.
C's efficiency is 9x, so time for C alone to finish the whole work = 1368x ÷ 9x = 152 hours.
Time for C to complete 50% of the work = 152 ÷ 2 = 76 hours.
Answer: 76 hours