Question : A, B and C together can complete a work in 12 days. A and B alone can do the same work in 36 days. In how many days can C alone complete the same work?
Option 1: 48
Option 2: 25
Option 3: 12
Option 4: 36
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Correct Answer: 36
Solution :
Given: A and B alone can do the same work in 36 days.
Let the total work = LCM of (12, 36, 36) = 36 units
Efficiency of A $=\frac{36}{36} = 1$ unit per day
Efficiency of B $=\frac{36}{36} = 1$ unit per day
Efficiency of A, B, and C together $\frac{36}{12} = 3$ units per day
Now, the efficiency of C = 3 – 1 – 1 = 1 unit per day
Then, the time C takes to complete the whole task alone is $\frac{36}{1} = 36$ days
Hence, the correct answer is 36.
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