Question

A pipe can fill the tank in 24 hrs, while a leak is at two-third of the height of tank(from bottom) can empty upto that part in 4hrs.If it opens simultaneously and initially the tank is full,then when will be two-third is full?
A.9
B.12
C.8
D.10
​

Answer 1

Step-by-step explanation:

option c is answer because 2 3rd is out so in 24 hrs it fills but it leaks only 1 3rd so

24/3=8

Answer 2

Concept:

The term 'efficiency (mathematical)' because it applies to the realm of basic math may be defined as 'the ability to see a way for solution quickly and with little effort'.

Given:

we are guven the time taken by the pipe to fill the tank is $24hrs$ while a leak is in $\frac{2}{3}$ of height tank from bottom can empty is $4hrs$.

Find:

We have to search out the time when are going to be two-third tank is full.

solution:

Firstly, we are going to find the efficiency of pipe.

$\text{efficiency of pipe}=\frac{1}{24}$

Time is taken by leaked pipe to empty tank of $\frac{1}{3}$ part is $4$ hrs.

Now, we'll find the efficiency of leaked part.

$\begin{aligned}\text{efficiency of leaked pipe}&=\frac{\frac{1}{3}}{4}\\ &=\frac{1}{12}\end$

Further, we are going to find the combined efficiency of pipe fill the tank and leak within the pipe of part, we get

$\begin{aligned}\text{combined efficiency}&=\frac{1}{24}-\frac{1}{12}\\ &=\frac{-}{24}\end$

Here, the negative sign shows leak in pipe.

Time required by both pipes to empty $\frac{1}{3}th$ of a tank is

$\begin{aligned}\frac{\frac{1}{3}}{\frac{1}{24}}&=\frac{1}{3}\times \frac{24}{}\\ &=8\end$

Hence, the time taken to fill two-third tank is $8hrs$. So, option (c) is correct.

3SPJ3