Question

A can do a piece of work in $x$ days and B can do the same work in $x+16$ days. If both working together can do it in 15 days, find the value of $x$.

• A. 2.2, 3.8 secs
• B. 5.4,6.2 secs
• C. 0.25,1.25 secs
• D. 7,5 secs

Answer 1

The correct option is C

0.25,1.25 secs

Given: A can do a piece of work in $x$ days and B in $x+16$ days.
Work done by A in one day = $\frac{1}{x}$
Work done by B in one day = $\frac{1}{x+16}$
Work done by A and B together in one day = $\frac{1}{15}$
$\Rightarrow$ $\frac{1}{x}$ + $\frac{1}{x+16}$ = $\frac{1}{15}$
$\Rightarrow$ $\frac{2x+16}{x(x+16)}=\frac{1}{15}$
$\Rightarrow$ $x^2+16x=15(2x+16)$
$\Rightarrow$ $x^2-14x-240=0$
$\Rightarrow$ $x^2-24x+10x-240=0$
$\Rightarrow$ $x(x-24)+10(x-24)=0$
$\Rightarrow$ $(x-24)(x+10)=0$
$\Rightarrow$ $x=24orx=-10$
$\Rightarrow$ $x=24$ as $x$ cannot be negative.