The ratio of the efficiencies of A, B and C is 7 : 5 : 8. Working together, they can complete a piece of work in 42 days. B and C worked together for 21 days and the remaining work was completed by A alone. The whole work was completed in:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 102 days
Ratio of the efficiencies of A, B and C is 7 : 5 : 8
Suppose the efficiencies are 7x, 5x and 8x respectively.
They can complete a piece of work in 42 days:
Total work = (7x + 5x + 8x) × 42
= 840x
B and C worked together for 21 days:
Word done = (5x + 8x) × 21 = 273x
Hence,
Remaining work = 840x – 273x = 567x
Since remaining work was completed by A alone;
Time taken by A
= 567x/7x
= 81 days
Hence,
Total time = 21 + 81 = 102 days