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A milkman mixes 20 litres of water with ...

A milkman mixes 20 litres of water with 80 litres milk. After selling one-fourth of this mixture, he adds water to replenish the quality that he has sold. What is the current ratio of water to milk?

A

`2 : 3`

B

` 1 : 2`

C

` 1 : 3`

D

` 3 : 4`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will follow these instructions: ### Step 1: Determine the initial quantities of water and milk. The milkman mixes: - Water = 20 litres - Milk = 80 litres ### Step 2: Calculate the total mixture. Total mixture = Water + Milk = 20 litres + 80 litres = 100 litres ### Step 3: Calculate the amount sold. The milkman sells one-fourth of the mixture: Amount sold = (1/4) × 100 litres = 25 litres ### Step 4: Determine the composition of the sold mixture. The mixture consists of water and milk in the ratio of 20:80, which simplifies to 1:4. This means for every 5 parts of the mixture, 1 part is water and 4 parts are milk. - Total parts = 1 (water) + 4 (milk) = 5 parts - Water in the sold mixture = (1/5) × 25 litres = 5 litres - Milk in the sold mixture = (4/5) × 25 litres = 20 litres ### Step 5: Calculate the remaining quantities after selling. Remaining water = Initial water - Water sold = 20 litres - 5 litres = 15 litres Remaining milk = Initial milk - Milk sold = 80 litres - 20 litres = 60 litres ### Step 6: Replenish the water. The milkman adds water to replenish the quantity sold. He adds back the 5 litres of water that he sold. New quantity of water = Remaining water + Water added = 15 litres + 5 litres = 20 litres ### Step 7: Calculate the current ratio of water to milk. Current ratio of water to milk = Water : Milk = 20 litres : 60 litres ### Step 8: Simplify the ratio. To simplify the ratio: - Divide both sides by 20: - Water = 20/20 = 1 - Milk = 60/20 = 3 Thus, the simplified ratio of water to milk is 1:3. ### Final Answer: The current ratio of water to milk is **1:3**. ---
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