Question : Ram can complete a task in 15 days, Rohan in 25 days, and Rohit in 30 days. Rohan and Rohit worked together for 2 days and then, Rohit was replaced by Ram. In how many days altogether was the work completed?
Option 1: 10 days
Option 2: 8 days
Option 3: 12 days
Option 4: 7 days
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Correct Answer: 10 days
Solution :
Given:
Ram can complete a task in 15 days, Rohan in 25 days, and Rohit in 30 days.
Work done by Ram in 1 day $= \frac{1}{15}$
Work done by Rohan in 1 day $= \frac{1}{25}$
Work done by Rohit in 1 day $=\frac{1}{30}$
Rohan and Rohit worked together for 2 days.
Work done by (Rohan + Rohit) in 1 day $= \frac{1}{25}+\frac{1}{30}=\frac{11}{150}$
Work done by them in 2 days $= 2×\frac{11}{150}=\frac{11}{75}$
Work left = $1-\frac{11}{75}=\frac{64}{75}$
Then, Rohit was replaced by Ram.
Work done by (Rohan + Ram) in 1 day $= \frac{1}{25}+\frac{1}{15}=\frac{8}{75}$
So, the remaining work will take $\frac{\frac{64}{75}}{\frac{8}{75}}=8$ days
So, the total work will take (8 + 2) = 10 days
Hence, the correct answer is 10 days.
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