Question

If A and B can complete a work in $\frac{16}{3}$ minutes and if A takes 8 minutes more than B, then the time taken by B is .

• A. 8 minutes
• B. 4 minutes
• C. 16 minutes

Answer 1

The correct option is A 8 minutes

Let B take $x$ minutes to complete the work.
Then, the time taken by A to do the same is $x+8$ minutes.

$\therefore$ The amount of work completed by B in one minute $=\frac{1}{x}$ units and

the amount of work completed by A in one minute $=\frac{1}{x+8}$ units.

Given that A and B can complete the work in $\frac{16}{3}$ minutes.

$\Rightarrow$ The amount of work completed in one minute by A and B together $=\frac{3}{16}$ units

$\Rightarrow \frac{1}{x}+\frac{1}{x+8}=\frac{3}{16}$

$\Rightarrow \frac{x+8+x}{x(x+8)}=\frac{3}{16}$

$\Rightarrow 16\times (2x+8)=3x(x+8)$

$\Rightarrow 32x+128=3x^2+24x$

$\Rightarrow 3x^2-8x-128=0$

$\Rightarrow 3x^2-24x+16x-128=0$

$\Rightarrow 3x(x-8)+16(x-8)=0$

$\Rightarrow (3x+16)(x-8)=0$

$\Rightarrow x=\frac{-16}{3}\text{or}8$

Thus, the roots of the equation are $\frac{-16}{3}$ and 8. But since time cannot be negative, the time taken by B to complete the work is 8 minutes.