Question

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

(a) 30 days

(b) 35 days

(c) 40 days

(d) 45 days

Answer 1

Let time taken by B to complete a work be ${}^{\prime }{x}^{\prime }$ days.

Therefore, time taken by A to the work $=x+50\%x=1.5x$ days

Now,

Work done by B in one days $=\frac{1}{x}$ units

Work done by A in one day $=\frac{2}{3x}$ units

Thus, according to the question,

$\Rightarrow \frac{1}{x}+\frac{2}{3x}=\frac{1}{18}$

$\Rightarrow \frac{5}{3x}=\frac{1}{18}$

$\therefore x=\frac{5\times 18}{3}=30$

Hence, time taken by B to complete the work is $30$ days.