IPMAT Indore 2023 - QA (SA) Q11 Explanation

Explanation:

(24)

Let the total work be 20 units.

Given that Amisha can complete the work in 20 days.

∴ Her efficiency = work/time = 20 𝑢𝑛𝑖𝑡𝑠/20 𝑑𝑎𝑦𝑠 = 1 unit/day.

In 4 days, she will complete 1 × 4 = 4 units of work.

She returns on 9th day, work with half the original efficiency i.e., 1/2 units/day.

Along, with her co-worker, she completes the work in 12 days.

∴ Total work done = (1unit/day × 4days) + (1/2 +𝑥)𝑢𝑛𝑖𝑡/𝑑𝑎𝑦 × 12days = 20units,

where, x is taken as efficiency of her co-worker.

Solving the equation, we get 𝑥 = 5/6 unit/day

∴ Time taken by co-worker to complete the work alone = work/efficiency = 20 units/5/6 units/day

= 24 days. Ans