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Thomas filled the tank through three pipes X, Y and Z. Pipe X is kept open in continuation, pipe Y kept open for first 20 minutes and then he closed it. 5 minutes after pipe B was closed, Pipe C is opened and was kept open till the tank was full. Together all the 3 pipes X, Y and Z take 'a' minutes to fill the tank. Each pipe fills an equal share of the tank. also, it is known that if pipe X and Y are kept open throughout, the tank would be completely fill in 'a' minutes. How long will it take C alone to fill the tank?  

Thomas filled the tank through three pipes X, Y and Z. Pipe X is kept open in continuation, pipe Y kept open for first 20 minutes and then he closed it. 5 minutes after pipe B was closed, Pipe C is opened and was kept open till the tank was full. Together all the 3 pipes X, Y and Z take 'a' minutes to fill the tank. Each pipe fills an equal share of the tank. also, it is known that if pipe X and Y are kept open throughout, the tank would be completely fill in 'a' minutes. How long will it take C alone to fill the tank?   Correct Answer 45 minutes

Given∶

 

Pipe X, Y and Z together fill the tank in 'a' minutes.

Pipe X was opened after 'a' minutes.

Pipe Y was opened 20 min. and then closed.

After 5 min. of this, Z was opened till the tank was full.

Each pipe filled equal share of the tank.

When X and Y, both opened they can fill the tank in 'a' minutes.

Formula Used∶

An inlet can fill a tank in X min. and another inlet in Y min. If both the inlets are opened at the same time, the net part of the tank filled in one minute is

given by; (1/x + 1/y)

Calculation∶

X is kept open for all 'a' minutes and fills one third of the tank Or,

X should be able to fill the entire tank in '3a' minutes.

X and Y together can fill in 'a' minutes

Part of tank filled by X and Y together in one minute = 1/a

Part of tank filled by X alone = 1/3a

So, part of tank filled by Y alone = 1/a - 1/3a = 2/3a

Or, Y takes 3a/2 minutes to fill an entire tank.

To fill one-third the tank, Y will take a/2 minutes. Y is kept open for 20 minutes.

a/2 = a - 20

⇒ a = 40 minutes

X takes 3a minutes = 3 × 40 = 120 minutes

Y takes 3a/2 minutes = 3 × 40/2 = 60 minutes

X is kept open for all 40 minutes

Y is kept open for all 20 minutes

Z which is kept open for 40 - 25 = 15 minutes

In 18 minutes pipe Z fills 1/3 of the tank.

To fill whole tank Z will take 15 × 3 = 45 minutes

∴ Z alone take 45 minutes to fill the tank.

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