Question

A takes 10 days less than the time taken by B to finish a piece of work If both A and B together can finish the work in 12 days the time taken by B to finish the work is

• A. 20 days
• B. 30 days
• C. 40 days
• D. 50 days

Answer 1

Answer: (B)

30 days

Let B alone finish the work $=xdays$.
And Alone finish the work $=(x-10)days$
A' s one day work $=\frac{1}{x-10}$
B's one day work $=\frac{1}{x}$
As it given tha
$(A+B)$ can finish work in 12 days
$\therefore (A+B)onedaywork=\frac{1}{12}$
$\Rightarrow A^{\prime }sonedaywork+B^{\prime }sonedaywork=\frac{1}{12}$
$\Rightarrow \frac{1}{x-10}+\frac{1}{x}=\frac{1}{12}$
$\Rightarrow \frac{x+x-10}{x(x-10)}=\frac{1}{12}$
$\Rightarrow \frac{2x-10}{x(x-10)}=\frac{1}{12}$
$\Rightarrow 12(2x-10)=x(x-10)$
$\Rightarrow 24x-120=x^2-10x$
$\Rightarrow x^2-10x-24x+120=0$
$\Rightarrow x^2-34x+120=0$
$\Rightarrow x^2-30x-4x+120=0$
$\Rightarrow x(x-30)-4(x-30)=0$
$\Rightarrow (x-4)(x-30)=0$
$\Rightarrow x=4orx=30$
$x\ne 4$
$\because ifx=4thenAalonecanfinishtheworkin=(4-10)=-6dayswhichisnotpossible$
$\therefore x=30days$
B alone can finish work in 30 days