Question
Download Solution PDFA, B and C together can complete a piece of work in 40/3 days. All three started working at it together and after 5 days A left. Then B and C together completed the remaining work in 17 days. Find the number of days (approximately) in which A alone can complete the total work.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A, B and C together can complete a piece of work in 40/3 days
All the three started working at it together and after 5 days A left. Then B and C together completed the work in 17 more days
Formula used:
Work = Efficiency × Time
Calculation:
Let a , b and c be the efficiencies of A , B and C respectively
According to the question,
(a + b + c) × 40/3 days = (a + b + c) × 5 days + ( b + c) × 17 days
40/3a + 40/3b + 40/3c = 5a + 5b + 5c + 17b + 17c
40/3a + 40/3b + 40/3c = 5a + 22b + 22c
25/3a = 26/3b + 26/3c
25/3a = 26/3(b + c)
25a = 26(b + c)
Ratio of a : (b + c) is 26 : 25
Let 25 and 26 be the efficiency of A and (B+C)
Total work = (a + b + c) × 40/3 days
= (25 + 26) × 40/3 days
= 51 × 40/3
= 680
Time taken to finish the work by A alone,
= 680/26 = 26 days (approx..)
∴ A alone can complete the total work in 26 days.
Last updated on Jun 30, 2025
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