Question

A is thrice as good as B and it therefore finish a piece of work in 60 days less than the time in which they can do it, working

• A. $22\frac{3}{4}days$
• B. $22\frac{1}{2}days$
• C. 24 days
• D. None of these

Answer 1

The correct option is B $22\frac{1}{2}days$

Let B takes x days to do the work. Then, A takes (x - 60) days to complete the work.
Since ratio of work done by A and B is 3 : 1, ratio of time taken by A and B is 1 : 3.
$Wehave,\frac{x-60}{x}=\frac{1}{3}$

$\Rightarrow$ 3(x - 60)=x or, x = 90.

$\therefore$ Time taken by B to finish the work = 90 days

and time taken by A to finish the work
$=\frac{90}{3}$
= 30 days.

$\therefore$ A and B, working together, will complete the work in
$\frac{xy}{x+y}days$

$=\frac{90\times 30}{90+30}days,i.e.\frac{45}{2}$

$or22\frac{1}{2}days.$