Question

An outlet pipe can empty a tank in 24 hours. A pipe that fills the tank at a rate of 2 ltr/min is opened together with the outlet pipe and the tank gets filled in 16 hours. What is the capacity of the tank?
1. 1152 ltr
2. 1000 ltr
3. 1252 ltr
4. 2000 ltr
5. 1352 ltr

Answer 1

Correct Answer - Option 1 : 1152 ltr

GIVEN:

Time taken by outlet pipe to empty = 24 hours

Time taken by both inlet and outlet pipes to fill = 16 hours

Rate of filling of inlet pipe = 2 ltr/min

EXPLANATION:

Time taken by outlet pipe to empty = 24 hours

Time taken by both inlet and outlet pipes to fill = 16 hours

LCM of 24 and 16 is 48 so, let the capacity of the tank be 48 units

Per hour efficiency of outlet pipe = \(\frac{48}{24}= -2\) units/hour (here '-' sign indicates outlet)

Per hour efficiency of both pipes together = \(\frac{48}{16}=3\) units/hour

Per hour efficiency of inlet pipe = Per hour efficiency of both pipes together - Per hour efficiency of the outlet pipe

\(\Rightarrow 3-(-2)=3+2=5 units/hour\)

5 units/hour = \(\frac1{12}\) units/min

 \(\frac1{12}\) units/min = 2 ltr/min

\(\frac1{12}\) units = 2 ltr 

1 unit = 24 ltr

Capacity of tank 48 units = 48 \(\times\) 24 = 1152 ltr