A vessel contains a mixture of Grape, Pineapple and Banana juices in the respectively ratio of 4 : 6 : 5. 15 litres of this mixture is taken out and 8 litres of grape juice and 2 litres of pineapple juice is added to the vessel. If the resultant quantity of grape juice is 10 litres less than the resultant quantity of pineapple juice, what was the initial quantity of mixture in the vessel ? ( in litres)

Solution(By Examveda Team)

Let quantity of grape, pineapple and banana juice in the mixture be 4x, 6x and 5x respectively
Total initial quantity of juice in the vessel
= 4x + 6x + 5x
= 15x litres
In 15 litres of juice,
Grape's juice = 4 litres
Pineapple's juice = 6 litres
Banana's juice = 5 litres
Resultant quantity of grape juice is 10 litres less than the resultant quantity of pineapple juice
$$\eqalign{ & \Rightarrow \left( {6x - 6 + 2} \right) - \left( {4x - 4 + 8} \right) = 10 \cr & \Rightarrow 6x - 4 - 4x - 4 = 10 \cr & \Rightarrow 2x - 8 = 10 \cr & \Rightarrow 2x = 10 + 8 \cr & \Rightarrow x = 9 \cr} $$
∴ Initial quantity of mixture
= 15x
= 15 × 9
= 135 litres