Akash can complete a piece of work alone in 8 days and Prakash can complete the same piece of work alone in 14 days. They started the work together, but Akash had to leave 4 days before the completion of the work. In how many days will the work complete?

Correct option is D

Let total work = LCM of 8 and 14 = 56 units Akash’s 1-day work = 56/8 = 7 units Prakash’s 1-day work = 56/14 = 4 units Let total time taken = x days Akash worked for (x − 4) days Work done = 7(x − 4) + 4x = 56 ⇒ 7x − 28 + 4x = 56 ⇒ 11x = 84 ⇒ x = 84/11 = 7 7/11 days
Oops! Looks like the marked answer in the image is 7 8/11, but correct value is 7 7/11, so there may be a key mismatch.
Explanation of options: (a) ✘ 7 10/11 is an overestimate (b) ✘ 7 12/11 = 8 1/11 — too high (c) ✔ Correct calculated time = 7 7/11 (d) ✘ 7 8/11 is slightly over, marked incorrectly