A tap can fill up a tank of 1250 litres in 4 hours, whereas another ta

1.	A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours. If all the three taps are opened simultaneously, then how much time will it take to fill the tank completely?1. 4.2 hours2. 4.5 hours3. 5 hours4. 4.8 hours
Answer» Correct Answer - Option 4 : 4.8 hours Given: Tap A can fill a tank in 4 hours Tap B can fill the same tank in 8 hours Tap C can empty the same tank in 6 hours Concept Used: If a tap can fill a tank in n hours then part of the tank filled in 1 hour is 1/n Calculation: Time is taken by tap A to fill the tank = 4 hours Tank filled by tap 1 in one hour = 1/4 part of the tank Time is taken by tap B to fill the tank = 8 hours Tank filled by tap 2 in one hour = 1/8 part of the tank Time is taken by tap C to empty the tank = 6 hours Tank emptied by tap 3 in one hour = 1/6 part of the tank So, the part of the tank filled in one hour when all three taps are opened simultaneously \(\frac{1}{4} + \frac{1}{8} - \frac{1}{6}\;part\) \( ⇒ \;\frac{{6 + 3 - 4}}{{24}}\;part\) \(⇒ \;\frac{5}{{24}}\;part\) ⇒ Time taken by 3 taps to fill the tank = 24/5 = 4.8 hours. ∴ time taken by three taps to fill the tank is 4.8 hours.

A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours. If all the three taps are opened simultaneously, then how much time will it take to fill the tank completely?1. 4.2 hours2. 4.5 hours3. 5 hours4. 4.8 hours

Answer» Correct Answer - Option 4 : 4.8 hours

Given:

Tap A can fill a tank in 4 hours

Tap B can fill the same tank in 8 hours

Tap C can empty the same tank in 6 hours

Concept Used:

If a tap can fill a tank in n hours then part of the tank filled in 1 hour is 1/n

Calculation:

Time is taken by tap A to fill the tank = 4 hours

Tank filled by tap 1 in one hour = 1/4 part of the tank

Time is taken by tap B to fill the tank = 8 hours

Tank filled by tap 2 in one hour = 1/8 part of the tank

Time is taken by tap C to empty the tank = 6 hours

Tank emptied by tap 3 in one hour = 1/6 part of the tank

So, the part of the tank filled in one hour when all three taps are opened simultaneously

\(\frac{1}{4} + \frac{1}{8} - \frac{1}{6}\;part\)

\( ⇒ \;\frac{{6 + 3 - 4}}{{24}}\;part\)

\(⇒ \;\frac{5}{{24}}\;part\)

⇒ Time taken by 3 taps to fill the tank = 24/5 = 4.8 hours.

∴ time taken by three taps to fill the tank is 4.8 hours.