Question : A can do $\frac{4}{5}$th of a work in 20 days and B can do $\frac{3}{4}$th of the same work in 15 days. They work together for 10 days. C alone completes the remaining work in 1 day. B and C together can complete $\frac{3}{4}$th of the same work in:
Option 1: 6 days
Option 2: 8 days
Option 3: 5 days
Option 4: 4 days
Correct Answer: 5 days
Solution :
Given :
A can do $\frac{4}{5}$th of a work in 20 days.
B can do $\frac{3}{4}$th of a work in 15 days.
Now,
A can complete the whole work $=20\times \frac{5}{4} = 25$ days
So, 1 day work of A $=\frac{1}{25}$
B can complete the whole work $=15\times \frac{4}{3} = 20$ days
So, 1 day work of B $=\frac{1}{20}$
Work done by A and B together in 10 days $=10\left ( \frac{1}{25} +\frac{1}{20} \right ) = \frac{9}{10}$
Remaining work = $1- \frac{9}{10} = \frac{1}{10}$
$\frac{1}{10}$th of the work be done by C in 1 day.
So, total work done by C in 10 days.
Work done by B and C together in 1 day = $\frac{1}{20}+\frac{1}{10}=\frac{3}{20}$
⇒ B and C will take to complete the $\frac{3}{4}$ of the work = $\frac{20}{3}\times \frac{3}{4} = 5$ days
Hence the correct answer is 5 days.
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