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
Efficiency of (A + B) is
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,
Hence, the correct answer is 60 days.
