Correct Answer - Option 2 : 120 days
Given:
A and B can do a work in 60 days and 75 days respectively
Both A and B work together for 10 days.
Calculation:
Work done by A in 1 day = 1/60
Work done by B in 1 day = 1/75
Work done by both (A + B) in 1 day = (1/60 + 1/75)
⇒ (5 + 4)/300
⇒ 9/300 = 3/100
Now, Work done by both (A + B) in 10 days = [10 × (3/100)] = 3/10
Remaining work = [1 – (3/10)] = 7/10
Work done by A in 6 day = [6 × (1/60)] = 1/10
Now, Remaining work = (7/10 – 1/10)
⇒ (7 – 1)/10 = (6/10) days
According to the question:
(A + C) × 6/10 = 24
⇒ (A + C) = (24 × 10)/6 = 40 days
Work done by both (A + C) in 1 days = 1/40
Work done by C in 1 day = (1/40 – 1/60)
⇒ (3 – 2)/120 = 1/120
∴ Total time work done by c in 120 days.