Question : Rohit and Mohit can do a piece of work in 4 days, while Ram and Shyam can do the same work in 12 days. In how many days will Rohit, Mohit, Ram, and Shyam do it together?
Option 1: 5 days
Option 2: 3 days
Option 3: 4 days
Option 4: 2 days
Correct Answer: 3 days
Solution :
Given,
Time taken by Rohit and Mohit to complete a piece of work = 4 days
We know, Efficiency = $\frac{1}{\text{Time taken}}$
⇒ Efficiency of Rohit and Mohit together = $\frac14$
Also, Ram and Shyam can do the same work in 12 days.
⇒ Efficiency of Ram and Shyam together = $\frac{1}{12}$
⇒ Efficiency of Rohit, Mohit, Ram, and Shyam together = $\frac{1}{4}+\frac{1}{12}=\frac{4}{12}=\frac13$
$\therefore$ Time taken by Rohit, Mohit, Ram, and Shyam together = 3 days
Hence, the correct answer is 3 days.
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