Question : A, B and C together can complete a work in 20 days. A and B together can complete the same work in 30 days. Then, C alone can complete the same work in how many days?
Option 1: 10 days
Option 2: 30 days
Option 3: 45 days
Option 4: 60 days
Correct Answer: 60 days
Solution :
Given: A, B, and C together can complete a work in 20 days and A and B together can complete the same work in 30 days.
Total work = Efficiency × Time
Total work is LCM of (20, 30) = 60 units
Efficiency of (A + B + C) is $\frac{60}{20}$ = 3
Efficiency of (A + B) is $\frac{60}{30}$ = 2
Then, the efficiency of C is [Efficiency of (A + B + C) – Efficiency of (A + B)] = 3 – 2 = 1
So, the time taken by C is given using the formula, $\frac{\text{Work}}{\text{Efficiency}}$ = $\frac{60}{1}$ = 60 days
Hence, the correct answer is 60 days.
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