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A can do 87.5% of the work in 35 days while B can do 65% of the same work in 23.4 days. If they work together, what fraction of the work will get done
Question

A can do 87.5% of the work in 35 days while B can do 65% of the same work in 23.4 days. If they work together, what fraction of the work will get done in 1 day?

A.

119\frac{1}{19}​​

B.

7120\frac{7}{120}​​

C.

19360\frac{19}{360}​​

D.

120\frac{1}{20}​​

Correct option is C

Given:
A can do 87.5% of the work in 35 days.
B can do 65% of the work in 23.4 days.

Solution:

A's Work
87.5% = 78\frac{7}{8}​ of work in 35 days
So full work = 35 × (87\frac{8}{7}​) = 40 days
A's 1 day work = 140\frac{1}{40}​​
B's Work
65% = 1320\frac{13}{20}​ of work in 23.4 days
So full work = 23.4×(2013)23.4 × (\frac{20}{13}) ​= 36 days
B's 1 day work = 136\frac{1}{36}​​
Combined 1 day work
=140+136 =36+4040×36 =9+10360 =19360\begin{aligned}&= \frac{1}{40} + \frac{1}{36} \\\ \\&= \frac{36 + 40}{40 \times 36} \\\ \\&= \frac{9 + 10}{360} \\\ \\&= \frac{19}{360}\end{aligned}​​
The fraction of work completed by A and B together in 1 day is 19360\frac{19}{360}​.

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