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Three pipes A, B and C are available to fill a tank. The time taken to fill the tank by A is 15 hours and by B is 10 hours. The time taken to fill the tank by both A and B together is equal to the time required for C to fill it. How much time is required to fill the tank by all the three pipes together?

Three pipes A, B and C are available to fill a tank. The time taken to fill the tank by A is 15 hours and by B is 10 hours. The time taken to fill the tank by both A and B together is equal to the time required for C to fill it. How much time is required to fill the tank by all the three pipes together? Correct Answer 3 hours

Given:  

Time taken by A to fill the tank = 15 hrs

Time taken by B to fill the tank = 10 hrs

Formula used:

If a pipe fills a tank in 'a' hours and an another fills the same tank in 'b' hours and the third one fills in 'c' hours then

Total work = LCM of the times taken by all of them = LCM of (a, b, c)

Efficiency of first pipe = LCM of (a, b, c)/a

Efficiency of second pipe = LCM of (a, b, c)/b

Efficiency of third pipe = LCM of (a, b, c)/c

Combined efficiency of them = efficiency of 1st pipe + efficiency of 2nd pipe + efficiency of 3rd pipe

Time taken to fill the tank = Total work/The combined efficiency of the pipes

Calculation:

A takes 15 hrs

B takes 10 hrs

Total work = LCM of (15, 10) = 30

One hour work of A = 30/15 = 2

One hour work of B = 30/10 = 3

One hour work of A + B = 3 + 2 = 5

∴ A + B takes 30/5 = 6 hours

C takes the same hours as A + B

⇒ C takes 6 hours

Now, A + B + C takes 2 + 3 + 5 = 10 hours

⇒ A + B + C together takes 30/10 = 3 hours to fill the tank

∴ required time is 3 hours.

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