Question

A tank can be filled in 10 hours. After a leak in its bottom, it takes 12 hours to fill the tank. Find the time taken by the leak to empty the full tank?

Answer 1

Given:

A tank can be filled in 10 hours. After a leak in its bottom, it takes 12 hours to fill the tank.

To find:

Time taken by leak to empty full tank

Calculation:

Whole tank is filled in 10 hours

Therefore , in 1 hour , amount of tank filled

$\rm{ = \dfrac{1}{10} \: part}$

In presence of leak , whole tank is filled in 12 hours,

Therefore in 1 hour , amount of tank filled

$\rm{ = \dfrac{1}{12} \: part}$

So, amount of water in tank leaked in 1 hour

$\rm{ = \dfrac{1}{10} - \dfrac{1}{12} }$

$\rm{ = \dfrac{6 - 5}{60} }$

$\rm{ = \dfrac{1}{60} \: part }$

Hence , total tank can be emptied by leak in:

$\rm{ = \dfrac{1}{ (\frac{1}{60}) } }$

$\rm{ = 60 \: hours}$

So, final answer is:

$\boxed{ \bf{time \: to \: empty \: tank \: by \: leak = 60 \: hours}}$

Answer 2

Given :-

• A tank can be filled in 10 hours.
• After a leak in its bottom, it takes 12 hours to fill the tank.

To Find :-

• Find the time taken by the leak to empty the full tank ?

Solution :-

LCM of 10 and 12 = 60 Litre = Let Capacity of Tank .

Than,

→ Time Taken to Fill the tank = 10 hours.

→ Capacity of Tank = 60 Litre .

So,

→ Efficiency of filling Pipe = (Capacity of Tank) / (Time Taken to Fill the tank) = (60/10) = 6 Litre / Hour.

Now, we have given That, because of the leak in bottom , it takes 12 hours to fill the tank.

So,

→ Efficiency of Pipe and Leak = (Capacity of Tank) / (Time Taken to Fill the tank by both) = 60/12 = 5 Litre / Hour.

As we can see now, Pipe alone fill 6 Litre / Hour but when Leak is their only 5 Litre water is going inside.

which conclude that, rest water is going outside per hour.

Therefore,

→ Efficiency of Leak = Efficiency of Pipe - Efficiency of Pipe and Leak

→ Efficiency of Leak = 6 - 5 = 1 Litre / Hour.

Hence,

→ The time taken by the Leak to empty the full tank = (Capacity of Tank) / (Efficiency of Leak) = 60/1 = 60 Hours. (Ans.)

∴ Leak alone can empty the full tank in 60 Hours.

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Shortcut :-

If a pipe can fill a tank in X hours and because of leak it takes Y hours ( where Y >X ) to full the tank, then the leak will emptied the whole tank in = 1 /{(1/X) - (1/Y)} Hours.

Given That :-

• X = 10 Hours.
• Y = 12 Hours.

So,

→ The time taken by the Leak to empty the full tank = 1/{(1/10) - (1/12)} = 1/{(6 - 5)/60} = 1/(1/60) = 60 Hours. (Ans.)

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