Question : Vijay and Sahil together complete a piece of work in 40 days, Sahil and Ranjit can complete the same work in 48 days and Ranjit and Vijay can complete the same in 60 days. In how many days can all three complete the same work while working together?
Option 1: 16 days
Option 2: 24 days
Option 3: 32 days
Option 4: 38 days
Correct Answer: 32 days
Solution :
Given: Vijay(V) and Sahil(S) complete a work in 40 days.
Sahil(S) and Ranjit(R) can complete the same work in 48 days.
Ranjit(R) and Vijay(V) can complete the same work in 60 days.
Total work is LCM of (40, 48, 60) = 240 units
Efficiency of Vijay and Sahil is $\frac{240}{40} = 6$
Efficiency of Sahil and Ranjit is $\frac{240}{48} = 5$
Efficiency of Ranjit and Vijay is $\frac{240}{60} = 4$
So, the efficiency of Vijay(V) and Sahil(S), Sahil(S) and Ranjit(R) and Ranjit(R) and Vijay(V) is (6 + 5 + 4) = 15.
Now, 2(V + S + R) = 15.
The efficiency of (V + S + R) is $\frac{15}{2}$.
So, the time taken by (V + S + R) is $\frac{\text{Total work}}{\text{Efficiency}}$.
$ \frac{240}{\frac{15}{2}} = 32$ days
Hence, the correct answer is 32 days.
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