Dinesh bought two radios for 1,920. He sold one at a profit of 20% and the other at a loss of 6 `2/3` % If the selling price of both radios are same, the cost prices of the two radios are

Options

A. 800 and 1,120
B. 840 and 1,080
C. 860 and 1,060
D. 900 and 1,020

Answer

To solve the problem step by step, we will first define the variables and then calculate the cost prices of the two radios based on the given conditions.

### Step 1: Define the total cost price of the radios
Dinesh bought two radios for a total of Rs. 1920.

### Step 2: Let the cost prices of the two radios be represented as:
- Cost price of Radio 1 = \( CP_1 \)
- Cost price of Radio 2 = \( CP_2 \)

From the problem, we know:
\[ CP_1 + CP_2 = 1920 \]

### Step 3: Selling price calculations
1. **Selling Price of Radio 1 (with 20% profit)**:
- Profit percentage = 20%
- Selling Price (SP) = \( CP_1 + 0.2 \times CP_1 = 1.2 \times CP_1 \)

2. **Selling Price of Radio 2 (with 6 2/3% loss)**:
- Loss percentage = \( 6 \frac{2}{3}\% = \frac{20}{3}\% \)
- Selling Price (SP) = \( CP_2 - \frac{20}{3} \times \frac{CP_2}{100} = CP_2 \left(1 - \frac{20}{300}\right) = CP_2 \left(1 - \frac{1}{15}\right) = CP_2 \left(\frac{14}{15}\right) \)

### Step 4: Set the selling prices equal
Since the selling prices of both radios are the same:
\[ 1.2 \times CP_1 = \frac{14}{15} \times CP_2 \]

### Step 5: Substitute \( CP_2 \) in terms of \( CP_1 \)
From Step 2, we can express \( CP_2 \) as:
\[ CP_2 = 1920 - CP_1 \]

Substituting this into the equation from Step 4:
\[ 1.2 \times CP_1 = \frac{14}{15} \times (1920 - CP_1) \]

### Step 6: Solve for \( CP_1 \)
Multiply both sides by 15 to eliminate the fraction:
\[ 15 \times 1.2 \times CP_1 = 14 \times (1920 - CP_1) \]

This simplifies to:
\[ 18 \times CP_1 = 26880 - 14 \times CP_1 \]

Combine like terms:
\[ 18 \times CP_1 + 14 \times CP_1 = 26880 \]
\[ 32 \times CP_1 = 26880 \]

Now divide both sides by 32:
\[ CP_1 = \frac{26880}{32} = 840 \]

### Step 7: Find \( CP_2 \)
Using the value of \( CP_1 \) to find \( CP_2 \):
\[ CP_2 = 1920 - CP_1 = 1920 - 840 = 1080 \]

### Final Answer
- Cost price of Radio 1 = Rs. 840
- Cost price of Radio 2 = Rs. 1080