Charging 30% above its production cost a radio maker puts a label of Indian rupee/Symbol ₹ 286 on a radio as its price. But at the time of selling it, he allows 10% discount on the labelled price. What will his gain be ?

Options

A. ₹ 257. 40
B. ₹ 254 . 40
C. ₹198
D. ₹ 37.40

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Cost Price (CP)
The radio maker charges 30% above the production cost. The labelled price (which is the marked price) is ₹286.

Let the cost price be \( CP \).

Since the radio maker charges 30% above the cost price, we can express this as:
\[ \text{Labelled Price} = CP + 30\% \text{ of } CP = CP + 0.3 \times CP = 1.3 \times CP \]
Thus, we can write:
\[ 1.3 \times CP = 286 \]

To find \( CP \), we rearrange the equation:
\[ CP = \frac{286}{1.3} \]

### Step 2: Calculate the Cost Price
Now, we perform the division:
\[ CP = \frac{286}{1.3} = 220 \]
So, the cost price of the radio is ₹220.

### Step 3: Calculate the Selling Price (SP)
The radio maker allows a 10% discount on the labelled price. Therefore, the selling price can be calculated as:
\[ \text{Selling Price} = \text{Labelled Price} - \text{Discount} \]
The discount is 10% of the labelled price:
\[ \text{Discount} = 10\% \text{ of } 286 = 0.1 \times 286 = 28.6 \]
Thus, the selling price is:
\[ SP = 286 - 28.6 = 257.4 \]

### Step 4: Calculate the Gain
Now, we can calculate the gain (profit) by subtracting the cost price from the selling price:
\[ \text{Gain} = SP - CP = 257.4 - 220 = 37.4 \]

### Conclusion
The gain made by the radio maker is ₹37.4.