Tick (✓) the correct answer:

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.

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