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In a 64 litre mixture of milk and water, the ratio of milk and water is 15 : 1. When 24 litre of mixture is removed and 5 litre of milk and water each is added, then find the difference between the quantity of milk and water in the final mixture.

In a 64 litre mixture of milk and water, the ratio of milk and water is 15 : 1. When 24 litre of mixture is removed and 5 litre of milk and water each is added, then find the difference between the quantity of milk and water in the final mixture. Correct Answer 35 litre

Given

The ratio of milk and water is 15 : 1

Let quantity of milk be 15x and water be x

Now

15x + x = 64

⇒ 16x = 64

⇒ x = 4

∴ Quantity of milk in initial mixture = 15x = 15 × 4 = 60 litre

And quantity of water in initial mixture = x = 4 litre

24 litre of mixture is removed

∴ The total new mixture = 64 - 24 = 40 litre

Again

The ratio of milk and water is 15 : 1

Let quantity of milk be 15x and water be x

Now

15x + x = 40

⇒ 16x = 40

⇒ x = 5/2

∴ Quantity of milk in new mixture = 15x = 15 × 5/2 = 37.5 litre

And quantity of water in new mixture = x = 2.5 litre

After adding 5 litre milk total quantity of milk = 37.5 + 5 = 42.5 litre

Also After adding 5 litre water total quantity of water = 2.5 + 5 = 7.5 litre

∴ The difference between the quantity of milk and water in the final mixture = 42.5 - 7.5 = 35 litre

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