A dairy farmer's can contains 6 litres of milk. His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1. How many litres of milk should the farmer add so that the milk and water are in the ratio 5 ∶ 1?

Question: A dairy farmer's can contains 6 litres of milk. His wife adds some water to it such that milk and water are in the ratio 4 ∶ 1. How many litres of milk should the farmer add so that the milk and water are in the ratio 5 ∶ 1?

Solution:
Given that,
Initially, 6 litres of milk (no water yet)
Wife adds water so that milk : water = 4 : 1
After that, farmer adds some milk so that the new ratio is 5 : 1

Now, find the amount of water added by the wife,
Milk : Water = 4 : 1
Milk = 6 litres
Let water = w litres
From the ratio we get,
⇒ 6/w = 4/1
⇒ 4w = 6
⇒ w = 6/4
⇒ w = 1.5
So, after wife adds water, mixture = 6 litres milk + 1.5 litres water.

And,
Let the farmer add x litres of milk
Now, Milk = 6 + x litres
Water = 1.5 litres
After farmer adds milk, new ratio is,
⇒ (6 + x)/1.5 = 5/1
⇒ 6 + x = 7.5
⇒ x = 7.5 - 6
∴ x = 1.5

The farmer should add 1.5 litres of milk.