Question

A can do a piece of work in ${}^{\prime }{x}^{\prime }$ days and $B$ can do the same work in ${}^{\prime }x+{16}^{\prime }$ days.If both working together can do it in $15$ days. Calculate $x$.

• A. $24$
• B. $25$
• C. $27$
• D. $Noneoftheabove$

Answer 1

The correct option is A $24$

Given A do a piece of work in x days and B do work in x+16 days

Then A one day work = $\frac{1}{x}$ days

AND B one day work =$\frac{1}{x+16}$days

Then Both one day work =$\frac{1}{x}+\frac{1}{x+16}=\frac{x+16+x}{x(x+16)}=\frac{2x+16}{x^2+16x}$

So both do work in $\frac{x^2+16x}{2x+16}days$

But both do work in 15 days

$\therefore \frac{x^2+16x}{2x+16}=15$

$\Rightarrow x^2+16x=30x+240$

$\Rightarrow x^2-14x-240=0$

$\Rightarrow x^2-24x+10x-240=0$

$\Rightarrow x(x-24)+10(x-24)=0$

$\Rightarrow (x-24)(x+10)=0$

Then $x-24=0,x=24$

And $x+10=0,x=-10$

But work done is not negative

Then work done =$24$ days