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 along complete the work ?

Answer 1

Let Manoj take x days to complete the work
And
Mohan x-16 days

I day's work of Manoj= $\frac{1}{x}$

I day's work of Mohan= $\frac{1}{(x-16)}$

I day's work of Manoj and Mohan together= $\frac{1}{x}+\frac{1}{x-16}$

Given,

$\frac{1}{x}+\frac{1}{x-16}=\frac{1}{15}$

$\frac{(x+x-16)}{(x^2-16x)}=\frac{1}{15}$

$30x-240=x^2-16x$

$x^2-46x-240=0$

$(x-40)(x-4)=0$

$x=40orx=4$

Here if x = 4 Mohan's work be in negative integers

$x=40$

$\therefore$ Manoj can do the work in 40 days and Mohan in 24 days