Amit is thrice as good a workman as Vinit and therefore is able to finish a work in 32 days less than Vinit. In how many days can the together complete the same work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 12 days.
The ratio of the efficiency of Amit and Vinit = 3 : 1
Efficiency ∝ 1/Time
So, the ratio of the time required to complete the work of Amit and Vinit = 1 : 3
The ratio difference = 3 - 1 = 2 units
According to the question, Amit can finish the work in 32 days less than Vinit.
So, 2 units → 32 days
1 unit → 16 days
3 units → 48 days
So, Amit and Vinit alone took 16 days and 48 days to finish the work, respectively.
1-day work of Amit = 1/16
1-day work of Vinit = 1/48
1-day work of Amit and Vinit = (1/16) + (1/48) = 4/48 = 1/12
Total time required = 12 days
Therefore, Amit and Vinit together complete the same work in 12 days.