A can contains a mixture of two liquids, grape juice and pineapple juice in the ratio 13 : 11. When 8 litres of the mixture is drawn off, and the can is filled with pineapple juice, the ratio becomes 13 : 14. How many litres of pineapple juice was initially contained in the can?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 33 litres.
Let total mixture = x litres
Initial ratio of grape : pineapple = 13 : 11
So, grape = (13/24) × x, pineapple = (11/24) × x
8 litres is removed — in same 13:11 ratio
Grape removed = (13/24) × 8 = 13/3 litres
Pineapple removed = (11/24) × 8 = 11/3 litres
After removing:
Grape = (13/24)x − 13/3
Pineapple = (11/24)x − 11/3
Then 8 litres of pineapple = (11/24)x − 11/3 + 8
New ratio = 13 : 14
So:
[(13/24)x − 13/3] ÷ [(11/24)x − 11/3 + 8] = 13 ÷ 14
⇒ x = 72 litres
Initial pineapple = (11/24) × 72 = 33 litres