A person sells wheat at a profit of 30%. If he reduces its selling price by Rs 60, then he suffers a loss of 10%. What was the initial selling price (in Rs) of the wheat?

Options

A. 195
B. 210
C. 180
D. 130

Answer

To solve the problem step by step, let's denote the cost price (CP) of the wheat as \( x \).

### Step 1: Calculate the Initial Selling Price (SP1)
The person sells the wheat at a profit of 30%. Therefore, the initial selling price (SP1) can be calculated as:
\[ SP1 = CP + 30\% \text{ of } CP = x + 0.3x = 1.3x \]

### Step 2: Calculate the Selling Price After Reduction (SP2)
If the selling price is reduced by Rs 60, the new selling price (SP2) becomes:
\[ SP2 = SP1 - 60 = 1.3x - 60 \]

### Step 3: Calculate the Selling Price at a Loss
When the selling price is reduced, the person incurs a loss of 10%. Therefore, the selling price at a loss (SP2) can also be expressed as:
\[ SP2 = CP - 10\% \text{ of } CP = x - 0.1x = 0.9x \]

### Step 4: Set Up the Equation
Now, we have two expressions for SP2:
1. From the reduction: \( SP2 = 1.3x - 60 \)
2. From the loss: \( SP2 = 0.9x \)

Setting these equal to each other gives:
\[ 1.3x - 60 = 0.9x \]

### Step 5: Solve for x
Now, we can solve for \( x \):
\[ 1.3x - 0.9x = 60 \]
\[ 0.4x = 60 \]
\[ x = \frac{60}{0.4} = 150 \]

### Step 6: Calculate the Initial Selling Price
Now that we have the cost price (CP), we can find the initial selling price (SP1):
\[ SP1 = 1.3x = 1.3 \times 150 = 195 \]

### Final Answer
The initial selling price of the wheat is Rs 195.

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