A is 3 times as fast as B and is, therefore, able to complete a work in 32 days lesser
than B. A and B, working together, can complete the work in _________.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e.12 days
Work Efficiency of A = 3 times B
Time taken by A to complete the work = 32 days lesser than B.
Total Time = Total Work/Total Efficiency
Work efficiency of A and B = 3 : 1
The ratio time taken = 1 : 3
Ratio difference = 3 - 1 = 2
The difference in time taken = 32 days
Ratio of 2 = 32 days
The ratio of 1 = 32/2 = 16 days
A alone completes the work in 16 days.
B completes in = 16 × 3 = 48 days
LCM of 16 and 48 = 48
Time in which both can complete the work together = Total Work/Total Efficiency = 48/(3 + 1) = 48/4 = 12 days