Question : A can finish a work in 25 days, and B can do the same work in 15 days. B worked for 10 days and left the job. A alone can finish the remaining work in how many days?
Option 1: $7 \frac{1}{3}$ days
Option 2: $6 \frac{1}{3}$ days
Option 3: $8 \frac{1}{3}$ days
Option 4: $5 \frac{1}{3}$ days
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Correct Answer: $8 \frac{1}{3}$ days
Solution :
Rate of A $= \frac{1}{25}$
Rate of B $=\frac{1}{15}$
Combined rate of A and B $=\frac{1}{25}+\frac{1}{15}$
According to the question,
B worked for 10 days.
The amount of work completed by B $ =10×\frac{1}{15}=\frac{2}{3}$ of the total work
⇒ Remaining work $=1-\frac{2}{3}=\frac{1}{3}$
A alone can finish the remaining work at the rate of $\frac{1}{25}$ of the total work per day.
$\therefore$ A will finish the remaining work in $\frac{\frac{1}{3}}{\frac{25}{3}}=\frac{25}{3}=8\frac{1}{3}$ days
Hence, the correct answer is $8\frac{1}{3}$ days.
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