Two pipes A and B running together can fill a tank in 6 minutes. If pipe A takes 5 minutes less than B to fill the tank, what is the time taken by pipe B to fill the tank alone ?

15 min

The correct answer is option (1) : 15 min

Let pipe B take x min to fill the tank alone , then pipe A will take (x-5) min to fill the tank alone.

So, part of the tank filled by pipe B in 1 min$=\frac{1}{x}$

Part of tank filled by pipe A in 1 min $=\frac{1}{x-5}$

Given that both pipes A and B together fill the tank in 6 min

$\frac{1}{x}+\frac{1}{x-5}=\frac{1}{6}$

$\frac{x-5+x}{x(x-5)}=\frac{1}{6}$

$x^2-17x+30=0$

$x-15x-2x+30=0$

$x(x-15)-2(x-15)=0$

$(x-15)(x-2)=0$

$x=2, 15 $but $x > 5$

$x=15$

Hence, the time taken by pipe B to fill the tank alone is 15 min.