To address this problem, let's tackle it through clear, step-by-step reasoning:
1. Define the Cost Price (CP):
Let's assume the cost price (the amount the shopkeeper paid to get the radio) is CP.
2. Determine the Marked Price (MP):
The shopkeeper aims to make a profit of 30%. This means the Marked Price must include an additional 30% on top of the Cost Price:
[tex]\[
MP = CP + 30\% \text{ of } CP = CP + 0.3 \times CP = 1.3 \times CP
\][/tex]
3. Account for the Discount:
The shopkeeper decides to give a discount of Rs 30 on the Marked Price. Subtracting this discount from the Marked Price, we get the Selling Price (SP) after discount:
[tex]\[
SP \text{ after discount} = MP - \text{discount} = 1.3 \times CP - 30
\][/tex]
4. Calculate the New Profit:
Profit is computed as the difference between the Selling Price after discount and the Cost Price:
[tex]\[
\text{Profit after discount} = SP \text{ after discount} - CP = (1.3 \times CP - 30) - CP = 0.3 \times CP - 30
\][/tex]
5. Given Profit Condition:
According to the problem, we need to find conditions to meet the profit expectations. Most likely, we'll solve for specific values that ensure clarity.
6. Given Potential Values and Result Interpretation:
If we were to solve it with given potential assumptions:
- Marked Price calculated would be: [tex]\( MP = 130 \text{ units} \)[/tex]
- Selling Price after discount: [tex]\( SP \text{ after discount} = 100 \text{ units} \)[/tex]
- Profit after discount: [tex]\( \text{New Profit} = 0)
\square = 0 \% \)[/tex]
Thus, observations reveal initially when cost alignment assured calculating scenarios, Cost Price would be numerically equivalent to accurate MP computations reflective in procedures detailed above.
To summarize succinctly:
1. Marked Price (MP) reaches Rs 130 under 30% profit,
2. Selling Price (SP) after Rs 30 discount correctly averages Rs 100,
3. Results resultantly yield eventual profitability configurations to 0% margins.
