Question : Benny can do a piece of work in 24 days. Chethan and David can do the same work individually in 36 and 48 days, respectively. All of them begin the work together. However, Benny leaves the work 4 days before the completion of work and Chethan leaves the work 10 days before the completion of the work. David worked till the end and completed the work. Find the number of days in which the work was completed.
Option 1: 16
Option 2: 20
Option 3: 18
Option 4: 15
Correct Answer: 16
Solution :
The rates of work per day at which Benny, Chethan, and David can complete the work are $\frac{1}{24}$,$\frac{1}{36}$, and $\frac{1}{48}$ respectively.
Let the total time taken to complete the work be $T$ days.
Benny worked for ($T - 4$) days, Chethan worked for ($T - 10$) days, and David worked for $T$ days.
The total work done is equal to 1 (as we're considering the whole work as one unit).
According to the question,
$\frac{T - 4}{24} + \frac{T - 10}{36} + \frac{T}{48} = 1$
⇒ $ \frac{6T-24+4T-40+3T}{144} = 1$
⇒ $\frac{13T}{144} = 1 + \frac{64}{144}$
⇒ $T=16$ days
Hence, the correct answer is 16.
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