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

Options

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

Answer

To find the cost price ratio of the two mixers purchased by Priya, we can follow these steps:

### Step 1: Define Variables
Let the cost price of Mixer 1 be \( X \) and the cost price of Mixer 2 be \( Y \). According to the problem, the total cost price of both mixers is:
\[ X + Y = 1500 \]

### Step 2: Calculate Profit and Loss
Priya made a profit of 9% on Mixer 1 and a loss of 6% on Mixer 2. The selling price (SP) for each mixer can be calculated as follows:
- Selling Price of Mixer 1:
\[ SP_1 = X + 0.09X = 1.09X \]
- Selling Price of Mixer 2:
\[ SP_2 = Y - 0.06Y = 0.94Y \]

### Step 3: Set Up the No Profit No Loss Condition
Since there is no overall profit or loss, the total selling price of both mixers must equal the total cost price:
\[ SP_1 + SP_2 = X + Y \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ 1.09X + 0.94Y = 1500 \]

### Step 4: Solve the Equations
Now we have a system of two equations:
1. \( X + Y = 1500 \)
2. \( 1.09X + 0.94Y = 1500 \)

From the first equation, we can express \( Y \) in terms of \( X \):
\[ Y = 1500 - X \]

Substituting this into the second equation:
\[ 1.09X + 0.94(1500 - X) = 1500 \]
Expanding this:
\[ 1.09X + 1410 - 0.94X = 1500 \]
Combining like terms:
\[ (1.09 - 0.94)X + 1410 = 1500 \]
\[ 0.15X + 1410 = 1500 \]
Subtracting 1410 from both sides:
\[ 0.15X = 90 \]
Dividing both sides by 0.15:
\[ X = \frac{90}{0.15} = 600 \]

### Step 5: Find Y
Now substitute \( X \) back into the equation for \( Y \):
\[ Y = 1500 - X = 1500 - 600 = 900 \]

### Step 6: Find the Ratio
The cost price ratio of Mixer 1 to Mixer 2 is:
\[ \frac{X}{Y} = \frac{600}{900} = \frac{2}{3} \]

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

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