Question

A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had a left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone finish the whole work ?

• A. 5 days , 8.5 days
• B. 2.5 days, 7.5 days
• C. 5 days, 15 days
• D. 3 days, 15 days,

Answer 1

The correct option is C 5 days, 15 days

Suppose A and B do the work in x and y days respectively Now work done by A in 2 days + work done by B in 9 days = 1
$\Rightarrow \frac{2}{x}+\frac{9}{y}=1$ Similarly $\frac{3}{x}+\frac{6}{y}=1$ Let $\frac{1}{x}=a$ and $\frac{3}{y}=b$ Then the equations become
2a + 9b = 1 .......(i)
3a + 6b = 1 .......(ii)
Performing (ii) x 2 - (i) x 3 we get (6a + 12b) - (6a + 27b) = 2 - 3
$\Rightarrow -15b=-1\Rightarrow b=\frac{1}{15}\Rightarrow x=15$ $\therefore$ Putting the value of b in (i)
$2a+9\times \frac{1}{15}=1\Rightarrow 2a=1-\frac{3}{5}=\frac{2}{5}\Rightarrow a=\frac{1}{5}\Rightarrow y=5$