Question

Mohan takes $16$ days less than Manoj to do a piece of work. If both working together can do it in $15$ days, in how many days will Mohan alone complete the work?

• A. $24days$
• B. $22days$
• C. $20days$
• D. $26days$

Answer 1

Answer: (A)

$24days$

Let Mohan and Manoj to do a piece of work be $x$.
Mohan takes $16$ days less than Manoj to do a piece of work = $\frac{1}{x-16}$
Mohan and Manoj working together = $\frac{1}{x}+\frac{1}{x-16}=\frac{1}{15}$
$\frac{2x-16}{x^2-16x}=\frac{1}{15}$
$30x-240=x^2-16x$
$x^2-46x+240=0$
Using $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ to find the value of $x$
$\Rightarrow \frac{46\pm \sqrt{(-46{)}^2-4\times 1\times (240)}}{2\times 1}$
$\Rightarrow \frac{46\pm \sqrt{1156}}{2}$
$\Rightarrow \frac{46\pm 34}{2}$
$x=40$, $x=6$
$x$ cannot be negative.
Mohan alone complete the work = $40-16=24$ hours.