Question

Two taps $A$ and $B$ fill a water tank together in $6$ hours. Alone, it takes tap $A$ $5$ hours less than $B$ to fill the same tank. How many hours does $A$ tap to fill the tank separately?

• A. $10$ hours
• B. $9$ hours
• C. $8$ hours
• D. $7$ hours

Answer 1

The correct option is A $10$ hours

Let $x$ be the time of $A$ tap
$x+5$ be the time of $B$ tap
As per the statement the equation becomes, $\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}$
Multiplying $x(x+5)$ on both sides to eliminate the denominator.
$6x+30+6x=x^2+5x$
$x^2-7x-30=0$
On factoring, we get
$(x-10)(x+3)=0$
$x=10$ or $-3$
A tap to fill the tank separately is $10$ hours.