Question

Two taps A and B can fill a cistern in 4 hours and 6 hours respectively. In the beginning, both taps are opened but after 2 hours first tap is turned off. How much longer will the tank take to fill?

Answer 1

Step-by-step explanation:

Given Two taps A and B can fill a cistern in 4 hours and 6 hours respectively. In the beginning, both taps are opened but after 2 hours first tap is turned off. How much longer will the tank take to fill?

• A cistern will be filled by tap A in 4 hours
• Therefore in 1 hour it will fill  1/4
• Also tap B can fill a cistern in 6 hours
• Therefore in 1 hour it will fill  1/6
• Now tap A and tap B together can fill in 1 hour will be 1/4 + 1/6 = 5/12
• Tap A and tap B together can fill in 2 hours = 2 x 5 / 12 = 5/6
• Remaining to fill will be 1 – 5 / 6 = 1 / 6
• Tap B can fill 1 in 6 hours
• Therefore 1/6 can be filled by tap B in 1 / 6 x 6 = 1 hour.

So the tank will take 1 hour more to fill the cistern.

Reference link will be

https://brainly.in/question/9340677

Answer 2

Given:

Tap A can fill the cistern in 4 hours.

Tap B can fill the cistern in 6 hours.

Both taps are turn on for 2 hours.

Tap A is turned off after 2 hours.

To Find:

How much longer does it need to fill the cistern after Tap A is turned off.

Solution

Find the fraction of the cistern Tap A can fill in 1 hour:

Tap A can fill the cistern in 4 hours

1 hour = 1/4 of the cistern

Find the fraction of the cistern Tap B can fill in 1 hour:

Tap B can fill the cistern in 6 hours

1 hour = 1/6 of the cistern

Find the fraction of the cistern is filled after two hours:

One hour → Tap A + Tap B = 1/4 + 1/6

One hour → Tap A + Tap B = 5/12

Two hours → Tap A + Tap B = 5/12 x 2

Two hours → Tap A + Tap B = 10/12

Two hours → Tap A + Tap B = 5/6

Find the remaining fraction of the cistern to be filled after 2 hours:

Remaining fraction of the cistern = 1 - 5/6

Remaining fraction of the cistern = 1/6

Find the amount of time Tap B needs to fill up the remaining of the cistern:

Time needed = 1/6 ÷ 1/6

Time needed = 1 hour

Answer: It takes another 1 hour to fill up the cistern.

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