Question

15. The capacity of a water tank is 1000 litres. It was 65% full of water. Some water taken out from the
tank and it found that the tank is now 48%, full of water. Find the volume of water taken out.​

Answer 1

${ \underline{ \bf{ \red{ \underline{Question:-}}}}}$

The capacity of a water tank is 1000 litres. It was 65% full of water. Some water taken out from the tank and it found that the tank is now 48%, full of water. Find the volume of water taken out.

${ \underline{ \bf{ \red{ \underline{Solution:-}}}}}$

{ According to question }

1. The capacity of a water tank is 1000 litres.
2. It was 65% full of water.
3. After some water taken out from the tank and it found that the tank is now 48% full of water.

Let, 100 % mean's 1000 liter water.

To find water in 65 % { we use percentage method }

Let, X liter water in 65 % .

Now,${ \sf{ \small{ \red \dagger{ \: Percentage \: of \: water = \frac{Amount \: of \: water }{Total \: amount \: of \: water} \times 100}}}}$

${ \sf{ \small{ \red \dagger{ \: 65 = \frac{X }{1000} \times 100}}}}$

${ \sf{ \small{ \red \dagger{ \: 65 = \frac{X }{10 { {00}}} \times {100}}}}}$

${ \sf{ \small{ \red \dagger{ \: 65 = \frac{X }{10 }}}} \: \: \: \: \: \: i.e.}$

${ \sf{ \small{ \red \dagger{ \: X } = {65 \times 10 }}}}$

${ \sf{ \small{ \red \dagger{ \: X } = {650 \: liter }}}}$

From ( 2 ) & ( 3 )

To find loss of water percent

Loss of water percent = { 65 - 48 } %

Loss of water percent = 17 %

Let, Y be the water of 17 %

Now,

${ \sf{ \small{ \red \dagger{ \: Percentage \: of \: water = \frac{Amount \: of \: water }{Total \: amount \: of \: water} \times 100}}}}$

${ \sf{ \small{ \red \dagger{ \: 17 = \frac{Y}{650} \times 100}}}}$

${ \sf{ \small{ \red \dagger{ \: 17 = \frac{Y}{65} \times 10}}}}$

${ \sf{ \small{ \red \dagger{ \: Y = \frac{17 \times 65}{10} }}}}$

${ \sf{ \small{ \red \dagger{ \:Y = 110.5 \: liter}}}}$

Subtract value of Y from value of X to get 48 % water

=> 48 % water = X - Y

=> 48 % water = 650 - 110.5

=> 48 % water = 539.5 liter

Hence, 539.5 liter water remain in tank and 110.5 liter water taken out from tank.

To find volume of 110.5 liter water

${ \dashrightarrow{\bf{ \frac{110.5}{1000} = 110.5 \times {10}^{ - 3} \: {m}^{3} }}}$

Hence, 110.5 × 10^ -3 m³ water taken out from tank.