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The ratio of water and milk in a 30 lite...

The ratio of water and milk in a 30 liter mixture is `7 : 3`. Find the quantity of water to be added to the mixture in order to make this ratio `6 : 1`.

A

30

B

32

C

33

D

35

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find out how much water needs to be added to a 30-liter mixture of water and milk, where the initial ratio of water to milk is 7:3, in order to change that ratio to 6:1. ### Step-by-Step Solution: 1. **Identify the initial quantities of water and milk:** - The total mixture is 30 liters. - The ratio of water to milk is 7:3. - To find the total parts in the ratio: \( 7 + 3 = 10 \) parts. - Each part is equal to \( \frac{30 \text{ liters}}{10} = 3 \text{ liters} \). 2. **Calculate the quantity of water and milk:** - Water = \( 7 \text{ parts} \times 3 \text{ liters/part} = 21 \text{ liters} \) - Milk = \( 3 \text{ parts} \times 3 \text{ liters/part} = 9 \text{ liters} \) 3. **Set up the new ratio:** - We want the new ratio of water to milk to be 6:1. - Let the amount of water added be \( x \) liters. - The new quantity of water will be \( 21 + x \) liters. - The quantity of milk remains the same at 9 liters. 4. **Formulate the equation based on the new ratio:** - According to the new ratio \( \frac{21 + x}{9} = 6 \). - Cross-multiply to solve for \( x \): \[ 21 + x = 6 \times 9 \] \[ 21 + x = 54 \] 5. **Solve for \( x \):** - Subtract 21 from both sides: \[ x = 54 - 21 \] \[ x = 33 \] 6. **Conclusion:** - The quantity of water to be added to the mixture is **33 liters**.
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