UGC NET CSE | October 2020 | Part 1 | Question: 25

Question

Three pipes fill a tank in $4$ hours. If two of them take $8$ and $12$ hours each to fill the tank, how many hours will the third pipe take to fill the tank?

• A. $6$ hours
• B. $15$ hours
• C. $18$ hours
• D. $24$ hours

Answer 1

Let $A$, $B$ and $C$ be three pipes, then according to question

Part of tank which three of them fills in $1$ hr = $ \frac{1}{A} + \frac{1}{B}+ \frac{1}{C} =\frac{1}{4}$

Similarly $\frac{1}{A}= 8, \frac{1}{B}= 12$ then 

$\frac{1}{C} = \frac{1}{4}- (\frac{1}{8}+\frac{1}{12})$

$\frac{1}{C}= \frac{1}{24}$

Option D) is correct