Question

a tank was 7/12 th part filled with water.in adding 12 l of water to it ,1/6th of the space was till left empty.what is the total quantity of water required to fill up the tank when it's empty​

Answer 1

Given : a tank was 7/12 th part filled with water

adding 12 l of water to it , 1/6th of the space was still left empty.

To Find :  total quantity of water required to fill up the tank when it's empty​

Solution:

Let say Tank capacity  = 12C  litre

a tank was 7/12 th part filled  with water =  ( 7/12)12C  = 7C  litre

12 l of water  added to it hence water in tank = 7C + 12 lire

Space left empty = 12C - (7C + 12)

= 5C - 12 litre

Space left empty = (1/6)12C  = 2C  litre

Equate

5C - 12 = 2C

=>  3C = 12

=> C = 4

=> 12C = 48

Tank capacity = 48 litre

water required to fill up the tank when it's empty​ = 48 litre

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Answer 2

SOLUTION

GIVEN

• A tank was $\displaystyle \sf{ \frac{7}{12} \: th}$ th part filled with water

• In adding 12 l of water to it , $\displaystyle \sf{ \frac{1}{6} }$ th of the space was till left empty

TO DETERMINE

The total quantity of water required to fill up the tank when it's empty

EVALUATION

Let the total quantity of water required to fill up the tank when it's empty = x litre

Now it is given that the tank was $\displaystyle \sf{ \frac{7}{12} \: th}$ part filled with water

So amount of water

$\displaystyle \sf{ = \frac{7x}{12} \: \:litre}$

Now 12 l of water was added to it

Now the total amount of water

$\displaystyle \sf{ = \bigg(\frac{7x}{12} + 12 \bigg) \: \:litre}$

Here it is stated that $\displaystyle \sf{ \frac{1}{6} }$ of the space was till left empty

So the the space which was filled with water

$\displaystyle \sf{ = \bigg(1 - \frac{1}{6} \bigg) \: }$

$\displaystyle \sf{ = \frac{5}{6} }$

So the total amount of water in the tank

$\displaystyle \sf{ = \frac{5x}{6} \: \:litre}$

So by the given condition

$\displaystyle \sf{ \frac{5x}{6} = \bigg(\frac{7x}{12} + 12 \bigg) }$

$\displaystyle \sf{ \implies \:10x = 7x + 144 }$

$\displaystyle \sf{ \implies \:3x = 144 }$

$\displaystyle \sf{ \implies \:x = \frac{144}{3} }$

$\displaystyle \sf{ \implies \:x = 48 }$

Hence the total quantity of water required to fill up the tank when it's empty = 48 litre

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