By selling an article for Rs 850, a shopkeeper gains 70%. To gain 30% what should be the selling price?

Options

A. 650
B. 720
C. 470
D. 570

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then determine the selling price (SP) needed to achieve a 30% profit.

### Step 1: Determine the Cost Price (CP)
Given that the selling price (SP) is Rs 850 and the profit percentage is 70%, we can use the formula for selling price:

\[ SP = CP \times \left(1 + \frac{P}{100}\right) \]

Where:
- \( SP = 850 \)
- \( P = 70 \)

Substituting the values into the formula:

\[ 850 = CP \times \left(1 + \frac{70}{100}\right) \]

This simplifies to:

\[ 850 = CP \times \left(1 + 0.7\right) \]
\[ 850 = CP \times 1.7 \]

Now, we can solve for CP:

\[ CP = \frac{850}{1.7} \]

Calculating this gives:

\[ CP = 500 \]

### Step 2: Calculate the Selling Price for 30% Profit
Now that we have the cost price, we need to find the selling price for a 30% profit. We will use the same formula for selling price:

\[ SP = CP \times \left(1 + \frac{P}{100}\right) \]

Where:
- \( CP = 500 \)
- \( P = 30 \)

Substituting the values into the formula:

\[ SP = 500 \times \left(1 + \frac{30}{100}\right) \]

This simplifies to:

\[ SP = 500 \times \left(1 + 0.3\right) \]
\[ SP = 500 \times 1.3 \]

Calculating this gives:

\[ SP = 650 \]

### Conclusion
To gain a 30% profit, the selling price should be Rs 650.

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