28
$A$ takes $6$ 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 $4$ days, find the time taken by $B$ alone to finish the work.
Show SolutionHide Solution↓
If time taken by $B$ be $x$ days, then $A$ takes $(x - 6)$ days
A.T.Q. $\frac{1}{x-6} + \frac{1}{x} = \frac{1}{4}$
$\implies x^2 - 14x + 24 = 0$
$\implies (x-12)(x-2) = 0$
$\implies x = 12$
$x = 2$ (rejected)
$\therefore B$ will take $12$ days to finish the work
A.T.Q. $\frac{1}{x-6} + \frac{1}{x} = \frac{1}{4}$
$\implies x^2 - 14x + 24 = 0$
$\implies (x-12)(x-2) = 0$
$\implies x = 12$
$x = 2$ (rejected)
$\therefore B$ will take $12$ days to finish the work