Solution:
Given:
Time is taken by A to complete the work = 16 days
Time is taken by B to complete the work = 24 days
Formula used:
Time is taken by A to complete the work = a days
Time is taken by B to complete the work = b days
Total unit of work = L.C.M of (a and b) units
Calculation:
Total unit of work = L.C.M of (16 and 24) = 48 units
Efficiency of A = 4816
= 3 units a day
Efficiency of B = 4824
= 2 units a day
According to the question,
Amount of work done by A on the first day = 3 units a day
Amount of work done by B on the second day = 2 units a day
In 2 days, the amount of work done = 5 units
On multiplying 9 on both sides,
In (2 × 9) days, the amount of work done = 5 × 9 units
In 18 days, the amount of work done = 45 units
Remaining amount of work = 48 - 45 = 3 units
Amount of work done by A on the first day = 3 units a day
Since the amount of work done by A on one day = 3 units a day
Therefore,
A will complete the 19th-day work.
Therefore,
The total time required to complete the work = 19 days
Therefore, '19 days' is the required answer.
