NIELIT 2016 DEC Scientist B - Section A: 49

Question

Two pipes $A$ and $B$ can fill a water tank in $20$ and $24$ minutes respectively and third pipe $C$ can empty at the rate of $3$ gallons per minute. If $A$, $B$ and $C$ opened together filled the tank in $15$ minutes, the capacity (in gallons) of the tank is:

• A. $60$
• B. $120$
• C. $150$
• D. $180$

Answer 1

Let the tank capacity $=x$  gallons.

Now, $\dfrac{x}{20} + \dfrac{x}{24} – 3 = \dfrac{x}{15}$

$\implies \dfrac{6x + 5x – 8x}{120} = 3$

$\implies 3x = 3 \times 120$

$\implies x = 120$ gallons.

So, the correct answer is $(B).$

Answer 2

Answer is B

A+B+C=$\frac{1}{15}$      A=$\frac{1}{20}$    B=$\frac{1}{24}$, we have to find C,

$\frac{1}{A+B+C}=\frac{1}{A}+\frac{1}{B}-\frac{1}{C}$    [as C is emptying the tank, so we will give “-”]

$\frac{1}{15}=\frac{1}{20}+\frac{1}{24}-\frac{1}{C}$

On solving, we wil get C = 40min.

Given, C can empty 3 gallons in 1min,

so, in 40min,  C can empty 3*40 = 120 gallons.