There are are two motor cycles (A and B) of equal cost price. Motorcycle A was sold at a profit of `14%` and Motorcycle B was sold for Rs 4,290 more than its cost price, The net .profit earned after selling both the motor cycles (A and B) is `20%`. What is the cost price of each motorcycle ?

Options

A. Rs 16,500
B. Rs 16.000
C. Rs 15,500
D. Rs 17,500

Answer

To solve the problem step by step, we will denote the cost price of each motorcycle as \( x \).

### Step 1: Define the cost price and selling prices
Let the cost price of each motorcycle (A and B) be \( x \).

- Selling price of Motorcycle A (SP_A) is given as:
\[ SP_A = x + 0.14x = 1.14x \]

- Selling price of Motorcycle B (SP_B) is given as:
\[ SP_B = x + 4290 \]

### Step 2: Calculate the total cost price and total selling price
The total cost price (CP_total) for both motorcycles is:
\[ CP_{total} = x + x = 2x \]

The total selling price (SP_total) for both motorcycles is:
\[ SP_{total} = SP_A + SP_B = 1.14x + (x + 4290) = 2.14x + 4290 \]

### Step 3: Use the profit percentage to set up an equation
According to the problem, the net profit earned after selling both motorcycles is 20%. Therefore, we can express this as:
\[ SP_{total} = CP_{total} + 0.20 \times CP_{total} \]
This can be rewritten as:
\[ SP_{total} = 1.20 \times CP_{total} \]

Substituting the values we found:
\[ 2.14x + 4290 = 1.20 \times 2x \]

### Step 4: Simplify the equation
Now, simplify the right side:
\[ 2.14x + 4290 = 2.4x \]

### Step 5: Rearrange the equation to solve for \( x \)
Rearranging gives:
\[ 2.4x - 2.14x = 4290 \]
\[ 0.26x = 4290 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 0.26 to find \( x \):
\[ x = \frac{4290}{0.26} = 16500 \]

### Conclusion
The cost price of each motorcycle is:
\[ \text{Cost Price} = Rs. 16,500 \]