A dishonest milkman mixed 1 litre of water for every 3 litres of milk and thus made up 36 litres of milk. If he now adds 15 litres of milk to the mixture, find the ratio of milk and water in the new mixture.
Question
A dishonest milkman mixed 1 litre of water for every 3 litres of milk and thus made up 36 litres of milk. If he now adds 15 litres of milk to the mixture, find the ratio of milk and water in the new mixture.
Solution
Step 1: Identify the initial quantities of milk and water in the mixture.
The milkman mixed 1 litre of water for every 3 litres of milk. So, in the 36 litres of mixture, the quantity of milk is 27 litres (3/4 of 36 litres) and the quantity of water is 9 litres (1/4 of 36 litres).
Step 2: Add the additional milk to the mixture.
The milkman adds 15 litres of milk to the mixture. So, the new quantity of milk is 27 litres + 15 litres = 42 litres.
Step 3: Find the new ratio of milk to water.
The quantity of water remains the same, 9 litres. So, the new ratio of milk to water is 42:9.
This ratio can be simplified by dividing both numbers by their greatest common divisor, which is 3. So, the simplified ratio is 14:3.
Therefore, the ratio of milk to water in the new mixture is 14:3.
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