Questions & Answers

Question

Answers

A. 12.5 min

B. 13.5 min

C. 14.5 min

D. 16.5 min

Answer
Verified

In the question, it is given that the first pipe fills the tank in 30 min and the second pipe fills the tank in 40 min.

We can write that a pipe filling the tank in x minutes means that the pipe can fill $\dfrac{1}{x}$ portion of the tank in 1 minute.

Using the above statement, we can find the portion of the tank filled by the pipes individually in 1 min.

Portion of the tank filled by the first pipe when x = 30 min is = $\dfrac{1}{30}$

Portion of the tank filled by the second pipe when x = 40 min is = $\dfrac{1}{40}$

Let us consider a pipe that fills $\dfrac{1}{x}$ portion of the tank in 1 minute is open for y minutes. Then the portion of the tank filled by it is given by $\dfrac{y}{x}$.

Let us consider that the first pipe is open for x minutes. The second pipe is open for the whole 18 minutes. The individual portions filled by the pipes, from the above relation, is given by

The portion of the tank filled by the first pipe in x minutes is $\dfrac{x}{30}$

The portion of the tank filled by the second pipe in 18 minutes is $\dfrac{18}{40}$

We can infer from the question that at the end of the 18 minutes, the tank is filled completely. From this, we can write that the sum of the portions filled by the two pipes will be equal to 1. Mathematically, it is written as

$\dfrac{x}{30}+\dfrac{18}{40}=1$

Subtracting $\dfrac{18}{40}$on both sides, we get

$\begin{align}

& \dfrac{x}{30}=1-\dfrac{18}{40} \\

& \dfrac{x}{30}=\dfrac{40-18}{40}=\dfrac{22}{40} \\

\end{align}$

Multiplying by 30 on both sides, we get

$x=\dfrac{22\times 30}{40}=\dfrac{22\times 3}{4}=5.5\times 3=16.5$