A vessel contains a mixture of Grape, Pineapple and Banana juices in the…
2025
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)
- A.
120 litres
- B.
150 litres
- C.
105 litres
- D.
135 litres
Attempted by 6 students.
Show answer & explanation
Correct answer: D
Concept: When a quantity is removed from a homogeneous mixture, it removes each ingredient in exactly the same ratio as the mixture's existing composition — removing L litres from a mixture in ratio a : b : c reduces each ingredient by L × a/(a+b+c), L × b/(a+b+c), and L × c/(a+b+c) respectively.
Application:
Let the initial quantities of grape, pineapple and banana juice be 4x, 6x and 5x litres (ratio 4 : 6 : 5), so the initial total is 15x litres.
Removing 15 litres of this mixture removes it in the same 4 : 6 : 5 ratio: 15 × 4/15 = 4 litres of grape, 15 × 6/15 = 6 litres of pineapple, and 15 × 5/15 = 5 litres of banana juice.
The remaining quantities become grape = 4x − 4, pineapple = 6x − 6, banana = 5x − 5.
Adding 8 litres of grape juice and 2 litres of pineapple juice updates them to grape = 4x − 4 + 8 = 4x + 4 and pineapple = 6x − 6 + 2 = 6x − 4.
The condition states the resultant grape juice is 10 litres less than the resultant pineapple juice: (6x − 4) − (4x + 4) = 10.
Simplifying: 2x − 8 = 10, so 2x = 18 and x = 9.
The initial quantity of the mixture is 15x = 15 × 9 = 135 litres.
Cross-check: With x = 9 the final grape quantity is 4(9)+4 = 40 litres and the final pineapple quantity is 6(9) − 4 = 50 litres — a difference of exactly 10 litres, confirming the initial mixture was 135 litres.