A takes 10 days 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,
A takes 10 days 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, find the time taken by B to finish the work.
Let B takes $x$ days to complete the work.
Therefore, A will take $(x-10)$ days.
$\therefore \frac{1}{x}+\frac{1}{(x-10)}=\frac{1}{12}$
$\Rightarrow \frac{(x-10)+x}{x(x-10)}=\frac{1}{12}$
$\Rightarrow \frac{2 x-10}{x^{2}-10 x}=\frac{1}{12}$
$\Rightarrow x^{2}-10 x=12(2 x-10)$
$\Rightarrow x^{2}-10 x=24 x-120$
$\Rightarrow x^{2}-34 x+120=0$
$\Rightarrow x^{2}-(30+4) x+120=0$
$\Rightarrow x^{2}-30 x-4 x+120=0$
$\Rightarrow x(x-30)-4(x-30)=0$
$\Rightarrow(x-30)(x-4)=0$
$\Rightarrow x=30$ or $x=4$
Number of days to complete the work by B cannot be less than that by A; therefore, we get:
$x=30$
Thus, B completes the work in 30 days.
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.