A man pays Rs. 6.40 per litre of milk. He adds water and sells the mixture at Rs. 8 per litre, thereby making 37.5% profit. The proportion of water to milk received by the customers is

• Cost price (CP) of milk = Rs. 6.40 per litre
• Selling price (SP) of mixture = Rs. 8 per litre
• Profit = 37.5% of CP
• Since water is free (no cost), profit is made by adding water to milk.

Let the quantity of milk be 1 litre, and let water added be x litres.

Total quantity of the mixture = 1 + x litres

Cost of 1 + x litres = Cost of 1 litre milk = Rs. 6.40

Selling price of 1 + x litres = Rs. 8 × (1 + x)

We use the profit formula:

Profit = SP - CP
37.5% profit ⇒ Profit = 0.375 × CP = 0.375 × 6.40 = Rs. 2.40

So, SP = CP + Profit = 6.40 + 2.40 = Rs. 8.80

But SP = 8 × (1 + x)
So,
8 × (1 + x) = 8.80
1 + x = 8.80 / 8 = 1.1
x = 1.1 - 1 = 0.1

Water = 0.1 litre
Milk = 1 litre
Ratio of water : milk = 0.1 : 1 = 1 : 10

Answer: 1 : 10