In a mixture, the ratio of a chemical X and water is 15 : 9. When 48 litres of this mixture is replaced with water, the ratio becomes 11 : 13. Find the quantity of water after replacement.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 97.5 liters.
Let the total quantity of the initial mixture be 8k liters (5k of chemical X and 3k of water)
The quantity of chemical X = (15/24) × 48 = 30 litres
The quantity of water = (9/24) × 48 = 18 litres
So, (5k - 30)/(3k + 30) = 11/13
⇒ 65k - 390 = 33k + 330
⇒ 32k = 720
⇒ k = 720 / 32 = 22.5
⇒ 3k + 30 = 3(22.5) + 30 = 67.5 + 30 = 97.5
Therefore, the quantity of water after replacement is 97.5 litres.