A bucket contains a mixture of milk and water in the proportion of 7 : 5. If 9 litres of milk is replaced by water, then the ratio becomes 7 : 9. How much mixture was there in the bucket initially?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 36 litres.
Let the amount of milk and water in the mixture be 7x and 5x respectively.
9 litres of milk is replaced by water, quantity of milk = 9 × 7/(7 + 5) = 5.25 litres
Quantity of water = 9 × 7/(7 + 5) = 3.75 litres
According to the given question,
(7x - 5.25)/5x - 3.75 + 9) = 7/9
⇒ 9(7x - 5.25) = 7(5x + 5.25)
⇒ 63x - 47.25 = 35x + 36.75
⇒ 28x = 84
⇒ x = 3
Initial quantity of mixture = 12x = 12 × 3 = 36 litres