If 7% of the sale price of an article is equivalent to 8% of its cost price and 9% of its sale price exceeds 10% of its cost price by 1, then what is the cost of the article?

Options

A. 400
B. 350
C. 300
D. 280

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided in the question.

### Step 1: Define Variables
Let:
- \( x \) = Cost Price of the article
- \( y \) = Sale Price of the article

### Step 2: Set Up the First Equation
According to the problem, 7% of the sale price is equivalent to 8% of the cost price. This can be expressed as:
\[ 0.07y = 0.08x \]
To eliminate the decimals, we can multiply through by 100:
\[ 7y = 8x \quad \text{(Equation 1)} \]

### Step 3: Set Up the Second Equation
The problem also states that 9% of the sale price exceeds 10% of the cost price by 1. This can be expressed as:
\[ 0.09y = 0.10x + 1 \]
Again, to eliminate the decimals, we multiply through by 100:
\[ 9y = 10x + 100 \quad \text{(Equation 2)} \]

### Step 4: Solve for \( y \) in Terms of \( x \)
From Equation 1, we can express \( y \) in terms of \( x \):
\[ y = \frac{8x}{7} \]

### Step 5: Substitute \( y \) into Equation 2
Now, substitute \( y \) from Equation 1 into Equation 2:
\[ 9\left(\frac{8x}{7}\right) = 10x + 100 \]
This simplifies to:
\[ \frac{72x}{7} = 10x + 100 \]

### Step 6: Clear the Fraction
To eliminate the fraction, multiply the entire equation by 7:
\[ 72x = 70x + 700 \]

### Step 7: Rearrange the Equation
Now, rearranging gives:
\[ 72x - 70x = 700 \]
\[ 2x = 700 \]

### Step 8: Solve for \( x \)
Dividing both sides by 2 gives:
\[ x = 350 \]

### Conclusion
The cost price of the article is \( \text{Rs. } 350 \).

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