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If A can complete a task in 10 days and B is 25% more efficient than A, how long (in days) will it take them to complete 60% of the task when they wor
Question

If A can complete a task in 10 days and B is 25% more efficient than A, how long (in days) will it take them to complete 60% of the task when they work together?

A.

2 1/3

B.

1 2/3

C.

2 2/3

D.

1 1/3

Correct option is C

Given:
Time taken by A = 10 days
B is 25% more efficient than A
Required task to complete = 60%
Formula Used:
Efficiency of B = Efficiency of A × (1 + Percentage100\frac{Percentage}{100}​)
Time = WorkCombined Rate\frac{Work}{Combined\ Rate}​​
Solution:
Let total work be 1 unit.
A's 1-day work (efficiency) = 110 \frac{1}{10}​​
Since B is 25% more efficient than A, B's efficiency is:
B's 1-day work = 110×(1+25100) \frac{1}{10} × (1 + \frac{25}{100})​​

B's 1-day work = 110×1.25=1.2510=1251000=18 \frac{1}{10} × 1.25 = \frac{1.25}{10} = \frac{125}{1000} = \frac{1}{8}

Combined 1-day work of A and B:
Rate = 110+18\frac{1}{10} + \frac{1}{8}​​

Rate = 440+540=940 \frac{4}{40} + \frac{5}{40} = \frac{9}{40}​​
We need to complete 60% of the task:
Work required = 60100=35 \frac{60}{100} = \frac{3}{5}​​

Time taken = 35940 \frac{\frac{3}{5}}{\frac{9}{40}}​​

Time taken = 35×409 \frac{3}{5} × \frac{40}{9}​​

Time taken = 12045=83 \frac{120}{45} = \frac{8}{3}​​=223= 2 \frac{2}{3}​ days

Final Answer
So the correct answer is (c) 

Exam Hall Method:

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