Priya purchased two mixers for % Rs. 1500 and made a profit of 9% on one and loss 6% on the other, But overall there is no profit or loss, then the cost price of mixers are in the ratio—

Options

A. `5:3`
B. `2:3`
C. `3:2`
D. `3:5`

Answer

To solve the problem, we need to find the cost price of the two mixers Priya purchased, given that she made a profit of 9% on one and a loss of 6% on the other, and overall there is no profit or loss. Let's denote the cost price of the first mixer as \( X \) and the cost price of the second mixer as \( Y \).

### Step-by-Step Solution:

1. **Set up the equations based on the given information**:
- The total cost price of both mixers is given as:
\[ X + Y = 1500 \]

2. **Calculate the selling price of each mixer**:
- For the first mixer (with a profit of 9%):
\[ \text{Selling Price of Mixer 1} = X + 0.09X = 1.09X \]
- For the second mixer (with a loss of 6%):
\[ \text{Selling Price of Mixer 2} = Y - 0.06Y = 0.94Y \]

3. **Set up the equation for overall selling price**:
- Since there is no overall profit or loss, the total selling price of both mixers equals the total cost price:
\[ 1.09X + 0.94Y = 1500 \]

4. **Now we have a system of equations**:
- From step 1: \( X + Y = 1500 \) (Equation 1)
- From step 3: \( 1.09X + 0.94Y = 1500 \) (Equation 2)

5. **Substitute \( Y \) from Equation 1 into Equation 2**:
- From Equation 1, we can express \( Y \) as:
\[ Y = 1500 - X \]
- Substitute this into Equation 2:
\[ 1.09X + 0.94(1500 - X) = 1500 \]

6. **Simplify the equation**:
\[ 1.09X + 1410 - 0.94X = 1500 \]
\[ (1.09X - 0.94X) + 1410 = 1500 \]
\[ 0.15X + 1410 = 1500 \]
\[ 0.15X = 1500 - 1410 \]
\[ 0.15X = 90 \]
\[ X = \frac{90}{0.15} = 600 \]

7. **Find \( Y \)**:
- Substitute \( X \) back into Equation 1:
\[ Y = 1500 - 600 = 900 \]

8. **Determine the ratio of \( X \) to \( Y \)**:
\[ \text{Ratio of } X \text{ to } Y = \frac{X}{Y} = \frac{600}{900} = \frac{2}{3} \]

### Final Answer:
The cost price of the mixers are in the ratio \( 2:3 \).