Renu sold article A at a loss of `10%`. She sold article B for price which was `25%` more than the selling price of article A. If she made a profit of `20%` on article B, by what percent is the cost price of article A more than that of article B?

Options

A. `6 2/3`
B. 4
C. 5
D. `2 1/6`

Answer

To solve the problem step by step, we will break down the information given and calculate the required values.

### Step 1: Define the Cost Price of Article A
Let the cost price of article A be \( CP_A = x \).

### Step 2: Calculate the Selling Price of Article A
Since Renu sold article A at a loss of 10%, the selling price \( SP_A \) can be calculated as:
\[ SP_A = CP_A - (10\% \text{ of } CP_A) = x - 0.1x = 0.9x = \frac{9x}{10} \]

### Step 3: Calculate the Selling Price of Article B
It is given that the selling price of article B is 25% more than the selling price of article A. Therefore:
\[ SP_B = SP_A + (25\% \text{ of } SP_A) = SP_A \times 1.25 = \frac{9x}{10} \times 1.25 = \frac{9x \times 5}{10 \times 4} = \frac{45x}{40} = \frac{9x}{8} \]

### Step 4: Relate Selling Price of Article B to its Cost Price
Renu made a profit of 20% on article B. Therefore, the selling price of article B can also be expressed in terms of its cost price \( CP_B \):
\[ SP_B = CP_B + (20\% \text{ of } CP_B) = CP_B \times 1.2 \]
Thus, we have:
\[ \frac{9x}{8} = CP_B \times 1.2 \]

### Step 5: Solve for Cost Price of Article B
From the equation above, we can solve for \( CP_B \):
\[ CP_B = \frac{9x}{8 \times 1.2} = \frac{9x}{9.6} = \frac{9x \times 10}{96} = \frac{90x}{96} = \frac{15x}{16} \]

### Step 6: Calculate the Difference in Cost Prices
Now we need to find out by what percent the cost price of article A is more than that of article B:
\[ \text{Difference} = CP_A - CP_B = x - \frac{15x}{16} = \frac{16x - 15x}{16} = \frac{x}{16} \]

### Step 7: Calculate the Percentage Increase
To find the percentage by which the cost price of article A is more than that of article B, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{CP_B} \right) \times 100 = \left( \frac{\frac{x}{16}}{\frac{15x}{16}} \right) \times 100 = \left( \frac{1}{15} \right) \times 100 = \frac{100}{15} = \frac{20}{3} \]
This simplifies to:
\[ \frac{20}{3} \approx 6.67\% \]

### Final Answer
The cost price of article A is \( 6 \frac{2}{3} \% \) more than that of article B.