Question

Alia can complete a assignment in 5 days and Baber can complete the same assignment
in 20 days. The time taken by both Alia and Baber to complete the assignment working
together is:
A) 2 days B) 3 days C) 4 days D) 5 days

Answer 1

Let us consider Alia's work first.

Alia completes the assignment in 5 days.

=> Part of completed in first day is 1 / 5 th of the work.

Therefore work done in 1 day is 1 / 5 => Equation 1

Baber completes assignment in 20 days.

=> Part of work completed in first day is 1 / 20 th of the work.

Therefore work done in one day is 1 / 20 => Equation 2

Adding equation 1 and 2 we get the amount of work done by them in the first day, if they worked together. This implies :

1 / 5 + 1 / 20 = 1 / x

Here x represents the total number of days taken to complete the work.

Taking LCM we get,

4 / 20 + 1 / 20 = 1 / x

=> 5 / 20 = 1 / x

=> 1 / 4 = 1 / x

Cross multiplying we get,

=> 1 * x = 1 * 4

=> x = 4

Hence the total number of days that will take if Alia and Baber work together is 4 days.