Question

In a vessel, there is a mixture of apple, orange and mango juices in the ratio of 3 : 5 : 4 respectively. a quantity of 12 litres from the mixture is replaced by 8 litres of apple juice. thereafter the quantities of apple and orange juices in the resultant mixture become same. find out the initial quantity of mixture in the vessel.

Answer 1

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Answer 2

Given:

Ratio of apple juice : orange juice : Mango juice = 3 : 5 : 4

12 litres of the mixture were removed.

8 litres of apples juice were added.

Thereafter, the quantity of apple and orange juice is the same.

To Find:

The initial quantity of mixture

Solution:

Define x:

Let x be the initial amount of mixture

12 litres were removed:

Amount of mixture left = x - 12

Find the amount of apple juice in the mixture:

$\text{Apple Juice } = \dfrac{3}{3 + 5 + 4} \times (x - 12)$

$\text{Apple Juice } = \dfrac{3 (x - 12)}{12}$

$\text{Apple Juice } = \dfrac{x - 12}{4}$

8 litres of apple juice were added:

$\text{Apple Juice } = \dfrac{x - 12}{4} + 8$

$\text{Apple Juice } = \dfrac{x - 12 + 32}{4}$

$\text{Apple Juice } = \dfrac{x + 20}{4}$

Find the amount of orange juice in the mixture:

$\text{Orange Juice } = \dfrac{5}{3 + 5 + 4} \times (x - 12)$

$\text{Orange Juice } = \dfrac{5 (x - 12)}{12}$

$\text{Orange Juice } = \dfrac{5x - 60}{12}$

The amount of apple juice and orange juice are the same:

$\dfrac{x + 20}{4} = \dfrac{5x - 60}{12}$

$12 ( x + 20) = 4( 5x - 60)$

$12x + 240 = 20x - 240$

$8x = 480$

$x.= 60$

Answer: There was 60 litres of mixture initially.