A cistern has a leak which would empty it in 8 h. A pipe is turned on

1.	A cistern has a leak which would empty it in 8 h. A pipe is turned on which admits 3 L in 1 min into the cistern and it is now emptied in 12 h. How many liters does the cistern hold?1. 4330 L2. 4320 L3. 4023 L4. 4230 L
Answer» Correct Answer - Option 2 : 4320 L Given: The cistern has a leak which would empty it in 8 h. Concept Used: Total work is LCM of work done by each pipe. Calculation: Work done by leak in 1 hour = 1 / 8 Total work done by both pipes in 1 hour = 1 / 12 Work done by the pipe in 1 h ⇒ (1 / 8 – 1 / 12) = 1 / 24 Work done by the pipe in 1 min ⇒ 1 / 24 × 1 / 60 ⇒ 1 / 1440 Volume of 1 / 1440 part = 3L Volume of the whole cistern = 3 × 1440 ⇒ Volume of the whole cistern = 4320 L ∴ The cistern holds 4320 Liters.

A cistern has a leak which would empty it in 8 h. A pipe is turned on which admits 3 L in 1 min into the cistern and it is now emptied in 12 h. How many liters does the cistern hold?1. 4330 L2. 4320 L3. 4023 L4. 4230 L

Answer» Correct Answer - Option 2 : 4320 L

Given:

The cistern has a leak which would empty it in 8 h.

Concept Used:

Total work is LCM of work done by each pipe.

Calculation:

Work done by leak in 1 hour = 1 / 8

Total work done by both pipes in 1 hour = 1 / 12

Work done by the pipe in 1 h

⇒ (1 / 8 – 1 / 12) = 1 / 24

Work done by the pipe in 1 min

⇒ 1 / 24 × 1 / 60

⇒ 1 / 1440

Volume of 1 / 1440 part = 3L

Volume of the whole cistern = 3 × 1440

⇒ Volume of the whole cistern = 4320 L

∴ The cistern holds 4320 Liters.

Discussion

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