Two pipes can fill a tank in 8 hours and 12 hours respectively. Both t

1.	Two pipes can fill a tank in 8 hours and 12 hours respectively. Both the pipes are opened together but due to a leakage in the tank, it takes 24 hours to fill the tank. If the tank is full, how long will the leakage take to empty the tank?1. 5 hours2. 6 hours3. 8 hours4. 12 hours5. 16 hours
Answer» Correct Answer - Option 2 : 6 hours Given: Two pipes can fill a tank in 8 hours and 12 hours respectively. With the leakage, it takes 24 hours to fill the tank. Concept: If a work can be completed in x hours, work done in 1 hour is 1/x If two pipes are opened together summation of their 1-hour work is the total work for 1 hour If leakage is there, its 1-hour work is subtracted from the total 1-hour work to get the total work done in an hour. Calculation: Total 1 hour work of the pipes = (1/8) + (1/12) = (10/48) Let the leakage can empty the tank in x hours Leakage 1 hour work = 1/x (10/48) – (1/x) = 1/24 ⇒ (1/x) = (10/48) – (1/24) ⇒ (1/x) = (10 – 2)/48 ⇒ (1/x) = (8/48) ⇒ (1/x) = (1/6) ⇒ x = 6 ∴ The leakage will take 6 hours to empty the full tank

Two pipes can fill a tank in 8 hours and 12 hours respectively. Both the pipes are opened together but due to a leakage in the tank, it takes 24 hours to fill the tank. If the tank is full, how long will the leakage take to empty the tank?1. 5 hours2. 6 hours3. 8 hours4. 12 hours5. 16 hours

Answer» Correct Answer - Option 2 : 6 hours

Given:

Two pipes can fill a tank in 8 hours and 12 hours respectively.

With the leakage, it takes 24 hours to fill the tank.

Concept:

If a work can be completed in x hours, work done in 1 hour is 1/x

If two pipes are opened together summation of their 1-hour work is the total work for 1 hour

If leakage is there, its 1-hour work is subtracted from the total 1-hour work to get the total work done in an hour.

Calculation:

Total 1 hour work of the pipes = (1/8) + (1/12) = (10/48)

Let the leakage can empty the tank in x hours

Leakage 1 hour work = 1/x

(10/48) – (1/x) = 1/24

⇒ (1/x) = (10/48) – (1/24)

⇒ (1/x) = (10 – 2)/48

⇒ (1/x) = (8/48)

⇒ (1/x) = (1/6)

⇒ x = 6

∴ The leakage will take 6 hours to empty the full tank