Profit after selling an article for 717 is `11(1/9)`% more then loss incurred when it is sold at Rs 527. What would be the selling price if he wants to earn a profit of 10%.

Options

A. a)Rs 678.7
B. b)Rs 577.7
C. c)Rs 398.7
D. d)Rs 979.7

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript and break down the calculations clearly.

### Step 1: Understand the Problem
We have two selling prices:
- Selling Price (SP1) = Rs 717 (where profit is made)
- Selling Price (SP2) = Rs 527 (where loss is incurred)

The profit from SP1 is `11(1/9)%` more than the loss from SP2.

### Step 2: Convert `11(1/9)%` to a Fraction
First, we convert `11(1/9)%` to an improper fraction:
- `11(1/9)%` = `11 + 1/9` = `99/9 + 1/9` = `100/9%`

### Step 3: Set Up the Equations
Let the Cost Price (CP) be denoted as `CP`.

1. Profit when selling at Rs 717:
\[ \text{Profit} = SP1 - CP = 717 - CP \]

2. Loss when selling at Rs 527:
\[ \text{Loss} = CP - SP2 = CP - 527 \]

According to the problem, the profit is `100/9%` more than the loss:
\[ 717 - CP = \left(1 + \frac{100}{900}\right) \times (CP - 527) \]
This simplifies to:
\[ 717 - CP = \frac{1000}{900} \times (CP - 527) \]

### Step 4: Simplify the Equation
Rearranging gives:
\[ 717 - CP = \frac{10}{9} \times (CP - 527) \]

### Step 5: Clear the Fraction
Multiply both sides by 9 to eliminate the fraction:
\[ 9(717 - CP) = 10(CP - 527) \]
Expanding both sides:
\[ 6453 - 9CP = 10CP - 5270 \]

### Step 6: Combine Like Terms
Rearranging terms gives:
\[ 6453 + 5270 = 10CP + 9CP \]
\[ 11723 = 19CP \]

### Step 7: Solve for CP
Dividing both sides by 19:
\[ CP = \frac{11723}{19} = 617 \]

### Step 8: Calculate Selling Price for 10% Profit
To find the selling price for a 10% profit:
\[ SP = CP + 10\% \text{ of } CP = CP \times \left(1 + \frac{10}{100}\right) = CP \times 1.1 \]
Substituting the value of CP:
\[ SP = 617 \times 1.1 = 678.7 \]

### Final Answer
The selling price if he wants to earn a profit of 10% is **Rs 678.7**.

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