A and B can complete a work in 12 days and 18 days, respectively. They worked together for 4 days, after which B was replaced by C and the remaining work was completeed by A and C in the next 4 days. In how many days will C alone can complte one third of the same work?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12 days
Given:
A and B can complete a work in 12 days and 18 days.
They worked together for 4 days, after which B was replaced by C.
The remaining work was completed by A and C in the next 4 days.
Concept used:
Total work = Time × Efficiency
Calculations:
Total work (LCM of 12 and 18) = 36 units
Efficiency of A = 36/12 = 3 units
Efficiency of B = 36/18 = 2 units
Total efficiency of A + B = 3 + 2 = 5 units
Work done in 4 days = 4 × 5 = 20 units
Remaining work = 36 - 20 = 16 units
Remaining work is done by (A + C) in 4 days = 16/4 = 4 units
We know, A + C = 4
Efficiency of C = 4 - 3 = 1 unit
Required time taken by C to complete one third of the total work = 36/(3 × 1) = 12 days