Question

A can do a piece of work in 12 days and B alone can do it in 16 days. They worked together on it for 3 days and then A left. How long B takes to finish the remaining work?
$
  A.{\text{ 8 days}} \\
  {\text{B. 5 days}} \\
  {\text{C. 7 days}} \\
  {\text{D. 9 days}} \\
 $

Answer 1

Hint- Here we will proceed by calculating work that can be done by A and B. Then we will add both individuals A and B work to find the remaining work of B.

Complete step-by-step answer:
Firstly, we will find work can be done by A and B in 1 day-
A can do part of work in 1 day $ = \dfrac{1}{{12}}$
B can do part of work in 1 day$ = \dfrac{1}{{16}}$
Now adding work of A and B in 1 day$ = \dfrac{1}{{12}} + \dfrac{1}{{16}} = \dfrac{7}{{48}}$
Adding work of A and B in 3 days$ = \dfrac{7}{{48}} \times 3 = \dfrac{7}{{16}}$
Remaining work $ = 1 - \dfrac{7}{{16}} = \dfrac{9}{{16}}$
B can do 1 work in days = 16
Also B can do $\dfrac{9}{{16}}$ work in days $ = \dfrac{9}{{16}} \times 16 = 9$
Hence B will take 9 days to finish the remaining work.
$ \Rightarrow $ Option D is correct.

Note- In order to solve this type of questions, one can make mistakes to omit the first step as the question is not directly asking about 1day work but we have to calculate it so that subtract it from 1 to get the required work by B.