Question

if tap A can fill in 15 hrs and tapB in 24 hrs and tapC canempty the tank in 30 hrs if all of themare opened together how long will they take to fill the tank​

Answer 1

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Answer 2

Given:

• Time taken by Tap A to fill the tank = 15 hours
• Time taken by Tap B to fill the tank = 24 hours
• Time taken by Tap C to empty the tank = 30 hours

To find:-

• Time taken to fill the tank if all the tanks are opened simultaneously.

Answer:-

Full/complete work is considered to be 1.

For Tap A:-

Work done in 15 hours = full work = 1

→ Part of work done in 1 hour = 1/15 ----( 1 )

For Tap B:-

Work done in 24 hours = full work = 1

→ Part of work done in 1 hour = 1/24 ----( 2 )

For Tap C:-

As tap C is emptying the tank, it is doing negative work.

Work done in 30 hours = negative(full work) = -1

→ Part of work done in 1 hour = - 1/30 ----( 3 )

When all the taps are opened simultaneously (Tap A + Tap B + Tap C) :-

Work done in 1 hour = 1/15 + 1/24 + (-1/30) [From ( 1 ), ( 2 ) and ( 3 )]

→ Work done in 1 hour = 1/15 + 1/24 - 1/30

→ Work done in 1 hour = [(8 + 5 - 4) / (120)]

→ Work done in 1 hour = 9/120

→ Work done in 1 hour = 3/40

So,

Time taken to do 3/40 part of work = 1 hour

→ Time taken to 1 (full/complete) work = 40/3 hours = 13⅓ hours.

Hence,

Time taken to fill the tank when all the taps are opened at the same time = 13⅓ hours Ans.