Mr A sold a goods, to Mr. B at 10% discounted value of printed rate. The discounted value is Rs1242. If 15% profit is earned on purchase rate by selling the goods at printed rate, what is the purchase rate?

Options

A. Rs 1242
B. Rs 1380
C. Rs 1280
D. Rs 1200

Answer

To find the purchase rate of the goods sold by Mr. A to Mr. B, we can follow these steps:

### Step 1: Determine the Printed Rate
We know that Mr. A sold the goods to Mr. B at a 10% discount, and the discounted value is Rs 1242.

Let the printed rate be \( P \).

Since Mr. A sold the goods at a 10% discount, we can express the discounted value as:
\[ \text{Discounted Value} = P - (10\% \text{ of } P) = P - 0.1P = 0.9P \]
Given that the discounted value is Rs 1242, we can set up the equation:
\[ 0.9P = 1242 \]

### Step 2: Solve for the Printed Rate
To find \( P \), we can rearrange the equation:
\[ P = \frac{1242}{0.9} \]
Calculating this gives:
\[ P = \frac{1242 \times 10}{9} = \frac{12420}{9} = 1380 \]
So, the printed rate \( P \) is Rs 1380.

### Step 3: Calculate the Purchase Rate
We are told that a 15% profit is earned on the purchase rate when selling at the printed rate. Let the purchase rate be \( C \).

The relationship between the selling price (printed rate), purchase rate, and profit can be expressed as:
\[ \text{Selling Price} = \text{Purchase Rate} + \text{Profit} \]
Given that the profit is 15% of the purchase rate:
\[ \text{Selling Price} = C + (15\% \text{ of } C) = C + 0.15C = 1.15C \]
Since the selling price is also equal to the printed rate, we can set up the equation:
\[ 1.15C = 1380 \]

### Step 4: Solve for the Purchase Rate
Now, we can solve for \( C \):
\[ C = \frac{1380}{1.15} \]
Calculating this gives:
\[ C = \frac{1380 \times 100}{115} = \frac{138000}{115} = 1200 \]
Thus, the purchase rate \( C \) is Rs 1200.

### Final Answer
The purchase rate is Rs 1200.

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