Question : A can do $\frac{1}{3}$ of a work in 30 days. B can do $\frac{2}{5}$ of the same work in 24 days. They worked together for 20 days. C completed the remaining work in 8 days. Working together A, B and C will complete the same work in:
Option 1: 15 days
Option 2: 10 days
Option 3: 18 days
Option 4: 12 days
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Correct Answer: 12 days
Solution :
A can do $\frac{1}{3}$ of a work in 30 days. So, A can finish the complete work in 90 days if working alone.
⇒ 1 day work of A = $\frac{1}{90}$
B can do $\frac{2}{5}$ of a work in 24 days. So, A can finish the complete work in 60 days if working alone.
⇒ 1 day work of B = $\frac{1}{60}$
So, 1 day work of both A and B = $\frac{1}{90}$ + $\frac{1}{60}$ = $\frac{1}{36}$
Work done by A and B together in 20 days = 20 × $\frac{1}{36}$ = $\frac{20}{36}$
Remaining work = 1 – $\frac{20}{36}$ = $\frac{4}{9}$
This work is done by C in 8 days.
So, 1-day work of C = $\frac{\frac{4}{9}}{8}$ = $\frac{1}{18}$
1 day work of (A + B + C) = $\frac{1}{36}$ + $\frac{1}{18}$ = $\frac{1}{12}$
So, the time taken by (A + B + C) = $\frac{1}{\text{1 day work of A, B, and C}}$ = $\frac{1}{\frac{1}{12}}$ = 12 days
Hence, the correct answer is 12 days.
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