CAT 2018 Slot 1 QA Question 5: When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together

Question

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together

Accepted Answer

Let A alone finish the job in a days.
Then B alone takes $1.25a = \dfrac{5a}{4}$ days.
A first completes half the work, so A works for $\dfrac{a}{2}$ days.
B finally completes 5% of the work, so B works for
$\dfrac{\dfrac{5}{100} 	imes 5a}{4} = \dfrac{a}{16}$ days.
$\dfrac{a}{2} + 4 + \dfrac{a}{16}