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The ratio of sprit and water is 2 : 5. I...

The ratio of sprit and water is 2 : 5. If the volume of solution is increased by 50% by adding sprit only. What is the resultant ratio of sprit and water ?

A

`9 : 10`

B

`12 : 15`

C

`11 : 10`

D

`3 : 4`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, follow these instructions: ### Step 1: Understand the initial ratio The initial ratio of spirit to water is given as 2:5. This means for every 2 parts of spirit, there are 5 parts of water. ### Step 2: Define the total parts The total parts of the solution can be calculated by adding the parts of spirit and water: \[ \text{Total parts} = 2 + 5 = 7 \text{ parts} \] ### Step 3: Assume a volume for calculation To simplify calculations, let's assume the total volume of the solution is 7 liters (this is equal to the total parts). Therefore: - Volume of spirit = \( \frac{2}{7} \times 7 = 2 \) liters - Volume of water = \( \frac{5}{7} \times 7 = 5 \) liters ### Step 4: Calculate the increase in volume The problem states that the volume of the solution is increased by 50% by adding spirit only. Calculate the increase: \[ \text{Increase} = 50\% \text{ of } 7 \text{ liters} = \frac{50}{100} \times 7 = 3.5 \text{ liters} \] ### Step 5: Determine the new volume of spirit Since we are adding only spirit, the new volume of spirit becomes: \[ \text{New volume of spirit} = 2 \text{ liters} + 3.5 \text{ liters} = 5.5 \text{ liters} \] ### Step 6: The volume of water remains the same The volume of water does not change, so it remains: \[ \text{Volume of water} = 5 \text{ liters} \] ### Step 7: Calculate the new ratio Now, we can calculate the new ratio of spirit to water: \[ \text{New ratio} = \frac{\text{Volume of spirit}}{\text{Volume of water}} = \frac{5.5}{5} \] To express this as a ratio, we can multiply both parts by 2 to eliminate the decimal: \[ \text{New ratio} = \frac{5.5 \times 2}{5 \times 2} = \frac{11}{10} \] Thus, the resultant ratio of spirit to water is: \[ \text{Resultant ratio} = 11:10 \] ### Final Answer The resultant ratio of spirit to water is **11:10**. ---
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