Question : A can finish a work in 15 days, B can finish the same work in 25 days. They work together for 5 days. The rest of the work is finished by A and C in 4 days. Then C alone can finish the work in:
Option 1: 18 days
Option 2: 24 days
Option 3: 20 days
Option 4: 21 days
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Correct Answer: 20 days
Solution :
Given, time taken by A and B to complete the work is 15 and 25 days respectively.
Efficiency of A = $\frac{1}{15}$ units/ day
Efficiency of B = $\frac{1}{25}$ units/ day
Work done in 5 days by A and B = $5(\frac{1}{15}+\frac{1}{25})=\frac{8}{15}$
So, Remaining work = $1-\frac{8}{15}=\frac{7}{15}$
Let the efficiency of C be $x$.
According to the question,
$\frac{7}{15}=4(\frac{1}{15}+x)$
$⇒4x=\frac{1}{5}$
$⇒x=\frac{1}{20}$
So, C can finish the work in 20 days
Hence, the correct answer is 20 days.
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