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A tank has two pipes. Pipe M is for filling the tank and pipe N is for emptying the tank. If pipe M takes 45 hours to completely fill the tank and pipe N takes 90 hours to empty the fully filled tank, then how many hours will they take to together fill the half empty tank completely?

A tank has two pipes. Pipe M is for filling the tank and pipe N is for emptying the tank. If pipe M takes 45 hours to completely fill the tank and pipe N takes 90 hours to empty the fully filled tank, then how many hours will they take to together fill the half empty tank completely? Correct Answer 45 hours

Given:

Time taken to fill a completely empty tank by pipe M = 45 hours

Time taken to empty a completely filled tank by pipe N = 90 hours

Concept Used:

If a pipe takes M hours to fill a completely empty tank, then the part of the tank filled by the pipe in 1 hour = 1/M

Similarly, if a pipe takes N hours to empty a completely empty tank, then the part of the tank emptied by the pipe in 1 hour = 1/N

But, the work done is negative while emptying the tank

Calculation:

Using the given conditions along with the concept used, we get:

Part of the tank filled by the pipe M in 1 hour = 1/45

Part of the tank emptied by the pipe N in 1 hour = 1/90

So, when both these tanks work together, the part of the tank they fill in one hour is obtained as:

1/45 – 1/90 = 1/90

Hence, the time taken by both the pipes to together fill the tank is obtained as:

1/(1/90) = 90 hours

Also, the time taken to fill the half empty tank completely, is obtained as:

90/2 = 45 hours 

∴ The time  the two pipes take to together fill the half empty tank completely is 45 hours

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