7% of S.P. of an article is equal to 8% of C.P. and 9% of S.P. is Rs 1 more than 10% of C.P. Find C.P. of article?

Answer

To solve the problem step by step, let's denote:

- \( S.P. \) = Selling Price
- \( C.P. \) = Cost Price

### Step 1: Set up the equations based on the problem statement.

From the first statement:
\[ 7\% \text{ of } S.P. = 8\% \text{ of } C.P. \]
This can be expressed mathematically as:
\[ \frac{7}{100} \times S.P. = \frac{8}{100} \times C.P. \]

### Step 2: Rearranging the first equation.

Multiplying both sides by 100 to eliminate the fractions:
\[ 7S.P. = 8C.P. \]

Now, we can express \( S.P. \) in terms of \( C.P. \):
\[ S.P. = \frac{8}{7} C.P. \]

### Step 3: Set up the second equation.

From the second statement:
\[ 9\% \text{ of } S.P. = 10\% \text{ of } C.P. + 1 \]
This can be expressed as:
\[ \frac{9}{100} \times S.P. = \frac{10}{100} \times C.P. + 1 \]

### Step 4: Rearranging the second equation.

Multiplying both sides by 100:
\[ 9S.P. = 10C.P. + 100 \]

### Step 5: Substitute \( S.P. \) from Step 2 into the second equation.

Substituting \( S.P. = \frac{8}{7} C.P. \) into the second equation:
\[ 9 \left(\frac{8}{7} C.P.\right) = 10C.P. + 100 \]

### Step 6: Simplifying the equation.

This gives us:
\[ \frac{72}{7} C.P. = 10C.P. + 100 \]

### Step 7: Eliminate the fraction.

To eliminate the fraction, multiply the entire equation by 7:
\[ 72C.P. = 70C.P. + 700 \]

### Step 8: Rearranging the equation.

Now, rearranging gives:
\[ 72C.P. - 70C.P. = 700 \]
\[ 2C.P. = 700 \]

### Step 9: Solve for \( C.P. \).

Dividing both sides by 2:
\[ C.P. = 350 \]

### Final Answer:
The Cost Price (C.P.) of the article is Rs 350.

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