A is 20% more efficient than B. How much time will they working together take to complete a job which A alone could have done in 29 days?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 1)

Answer 1

Given:

A is 20% more efficient than B.

Concept used:

1. Efficiency (work done per day) of workers is inversely proportional to the time taken by workers to complete a particular task.

2. If A and B take x and y days to complete a task independently, alone they will get the work done in = xy/(x + y) days

Calculation:

According to the concept,

To complete the job alone, B will take = 29 × (1 + 20%) = 34.8 days

Working together, they will complete the work in

⇒ (29 × 34.8) ÷ (29 + 34.8)

⇒ \(\frac{174}{11}\) days

∴ Working together, they will complete the work in \(\frac{174}{11}\) days.

Alternate Method

A is 20% more efficient than B, then efficiency of A : B = 120 : 100 = 6 : 5

A alone could have done in 29 days, then total work = (6 × 29) = 174 unit

If A and B together do the work then time takes = 174/(6 + 5) = 174/11 days