Question

Tap A can fill a tank in 6 hours, tap B can fill the tank in 4 hours and tap C can empty the tank in 12 hours. If all the taps are open , how much time would be required to fill the tank ?​

Answer 1

Answer:

1 hour

Step-by-step explanation:

Answer 2

Given:

✰ Tap A can fill a tank in 6 hours.

✰ Tap B can fill the tank in 4 hours.

✰ Tap C can empty the tank in 12 hours.

✰ All the taps are open together.

To find:

✠ How much time would be required to fill the tank ?

Solution:

Let's understand the concept first! First we will find tap A's 1 hour work and then tap B's 1 hour work. Then, we will add together work of tap A and B in 1 hour. After that we will find tap C's one hour work, then substract tap C's one hour work from the together work of tap A and B in 1 hour, to get the part of the tank to be filled. Using it we will find the time required to fill the tank.

Let's find out...✧

We will find one hour's work as,

✭ One hour's work = 1/no. of number required to fill the tank ✭

➛ Tap A's 1 hour work = 1/6 hours

➛ Tap B's 1 hour work = 1/4 hours

➛ Together work of tap A and tap B in 1 hour = 1/6 + 1/4

➛ Together work of tap A and tap B in 1 hour = ( 2 + 3)/12

➛ Together work of tap A and tap B in 1 hour = 5/12

Then,

➛ Tap C's 1 hour work = 1/12 hours

➤ If Tap A and B fills the tank and tap C can empty the tank = Together work of tap A and tap B in 1 hour - Tap C's 1 hour work

➤ If Tap A and B fills the tank and tap C can empty the tank = 5/12 - 1/12

➤ Tap A and B fills the tank and tap C can empty the tank = (5 - 1)/12

➤ Tap A and B fills the tank and tap C can empty the tank = 4/12

➤ Tap A and B fills the tank and tap C can empty the tank = 1/3

∴ 1/3 part of the tank can be filled in 1 hour

Now,

1 part of tank in x hours can be filled

x = (1×1)/1/12

x = 1/1/12

x = 1 × 12

x = 12 hours

∴ 12 hours would be required to fill the tank.

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