Question
Download Solution PDFA alone can finish a work in 15 days. A works only for the first two days and last two days. The rest work is done by B and the work is completed in 20 days. In how many days A and B together can finish the work?
Answer (Detailed Solution Below)
Detailed Solution
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A works for a total 4 days and B works for a total (20 - 4) = 16 days.
A can complete alone in 15 days.
So, on comparing total works
4A + 16B = 15A
16B = 11A
A/B = 16/11
Total work = 15A = 15×16 = 240
A + B = 240/(16 + 11) = 240/27 = 80/9
∴ The correct answer is 80/9.
Alternate Method
Given:
A alone can finish a work in 15 days.
A works only for the first two days and last two days.
The rest work is done by B and the work is completed in 20 days.
Concept used:
Efficiency = (Total work / Total time taken)
Efficiency = work done in a single day
Calculation:
Let total work is 60 units ( Lcm of 20 and 15)
The efficiency of A is
⇒ 60 / 15 = 4 unit
A does total 4 × 4 = 16 units
Remainig work , 60 - 16 = 44 units does by B in 16 days
Again, the Efficiency of B is,
⇒ 44 / 16 = 11/4 units
Total efficiency is 4+11/4 = 27/4
A and B does the work in,
60×4/ 27 = 80/9 days
∴ The correct option is 3
Last updated on Jul 10, 2025
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