Question : P, Q and R together can complete a work in 40 days. P and Q together can complete the same work in 90 days. Then R alone can complete the same work in how many days?
Option 1: 40 days
Option 2: 72 days
Option 3: 84 days
Option 4: 90 days
Correct Answer: 72 days
Solution :
Given: P, Q, and R together can complete a work in 40 days and P and Q together can complete the same in 90 days.
Total work = Efficiency × Time
Total work is LCM of (40, 90) = 360 units
Efficiency of (P + Q + R) is $\frac{360}{40}$ = 9
Efficiency of (P + Q) is $\frac{360}{90}$ = 4
Then, the efficiency of R = [Efficiency of (P + Q + R) – Efficiency of (P + Q)] = 9 – 4 = 5
So, the time taken by R is given using the formula, $\frac{\text{work}}{\text{efficiency}}$ = $\frac{360}{5}$ = 72 days
Hence, the correct answer is 72 days.
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