A container holds a mixture of Orange, Apple, and Guava juices in the ratio 5 : 7 : 4 respectively. 24 litres of this mixture is taken out, and then 10 litres of orange juice and 6 litres of guava juice are added to the vessel. If the resultant quantity of apple juice is 14 litres greater than the quantity of orange juice, what was the initial quantity of mixture in the vessel (in litres)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 216.
Let the initial quantities of Orange, Apple, and Guava juices be 5x, 7x, and 4x
Total initial mixture = 5x + 7x + 4x = 12x
Orange removed = × 24 = 7.5 litres
Apple removed = × 24 = 10..5 litres
Guava removed = × 24 = 6 litres
After removing the portions and adding 10 litres of orange juice and 6 litres of guava juice
Final Orange juice = (5x - 7.5) + 10 = 5x + 2.5
Final Apple juice = 7x - 10.5
Final Guava juice = (4x - 6) + 6 = 4x
⇒ (7x - 10.5) - (5x + 2.5) = 14
⇒ 2x - 13 = 14
⇒ 2x = 27
⇒ x = 13.5
Total initial mixture = 16x = 16 × 13.5 = 216 litres