Question:
Tick (✓) the correct answer:
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
Solution:
(a) 30 days
Let $B$ take $x$ days to complete the work.
Then A takes $\left(x+\frac{50}{100} x\right)=1.5 x$
A's 1 day's work $=\frac{1}{1.5 x}=\frac{2}{3 x}$
$B^{\prime} s 1$ day's work $=\frac{1}{x}$
$(A+B)$ takes 18 days to complete the work.
$(A+B)^{\prime} s 1$ day's net work $=\frac{1}{18}$
or $\frac{1}{18}=\frac{2}{3 x}+\frac{1}{x}$
$\Rightarrow \frac{1}{18}=\frac{5}{3 x}$
By cross - multiplication, we get:
$x=30$ days
$\therefore B$ alone will take 30 days to complete the work.