A person sold an article at a loss of 8% Had he sold it at a grain of 10.5% he would have received Rs 74 more. What is the cost price (in Rs) of the article ?

Options

A. 300
B. 400
C. 500
D. 100

Answer

To find the cost price of the article, we can follow these steps:

### Step 1: Define the variables
Let the cost price (CP) of the article be Rs X.

### Step 2: Calculate the selling price at a loss of 8%
When the article is sold at a loss of 8%, the selling price (SP) can be calculated as:
\[ SP = CP - (Loss\% \times CP) \]
\[ SP = X - (8\% \times X) \]
\[ SP = X - \frac{8}{100} \times X \]
\[ SP = X \left(1 - \frac{8}{100}\right) \]
\[ SP = X \left(\frac{92}{100}\right) \]
\[ SP = \frac{92X}{100} \]

### Step 3: Calculate the selling price at a gain of 10.5%
When the article is sold at a gain of 10.5%, the selling price can be calculated as:
\[ SP = CP + (Gain\% \times CP) \]
\[ SP = X + (10.5\% \times X) \]
\[ SP = X + \frac{10.5}{100} \times X \]
\[ SP = X \left(1 + \frac{10.5}{100}\right) \]
\[ SP = X \left(\frac{110.5}{100}\right) \]
\[ SP = \frac{110.5X}{100} \]

### Step 4: Set up the equation based on the information given
According to the problem, the difference between the selling prices at a gain of 10.5% and a loss of 8% is Rs 74. Therefore, we can set up the equation:
\[ \frac{110.5X}{100} - \frac{92X}{100} = 74 \]

### Step 5: Simplify the equation
Combining the fractions gives:
\[ \frac{110.5X - 92X}{100} = 74 \]
\[ \frac{18.5X}{100} = 74 \]

### Step 6: Solve for X
To isolate X, multiply both sides by 100:
\[ 18.5X = 7400 \]
Now, divide by 18.5:
\[ X = \frac{7400}{18.5} \]
Calculating this gives:
\[ X = 400 \]

### Conclusion
The cost price of the article is Rs 400.

---