Each of A and B sold their article at ₹ 1818 but A incurred a loss of `10%` while B gained by `1%`. What is the ratio of cost price of the articles of A to that of B?

Options

A. 101:90
B. 85:89
C. 81:75
D. none of these

Answer

To solve the problem step by step, we need to find the cost prices of articles A and B based on the information given about their selling prices and the profit/loss percentages.

### Step 1: Understand the Selling Price (SP)
Both A and B sold their articles at the same selling price (SP) of ₹1818.

### Step 2: Calculate the Cost Price (CP) of A
A incurred a loss of 10%. This means that the selling price is 90% of the cost price. We can express this mathematically as:
\[ SP_A = CP_A \times \left(1 - \frac{10}{100}\right) \]
\[ 1818 = CP_A \times 0.90 \]

Now, we can solve for \( CP_A \):
\[ CP_A = \frac{1818}{0.90} \]
\[ CP_A = 2020 \]

### Step 3: Calculate the Cost Price (CP) of B
B gained a profit of 1%. This means that the selling price is 101% of the cost price. We can express this mathematically as:
\[ SP_B = CP_B \times \left(1 + \frac{1}{100}\right) \]
\[ 1818 = CP_B \times 1.01 \]

Now, we can solve for \( CP_B \):
\[ CP_B = \frac{1818}{1.01} \]
\[ CP_B \approx 1800 \]

### Step 4: Find the Ratio of Cost Prices
Now we need to find the ratio of the cost price of A to the cost price of B:
\[ \text{Ratio} = \frac{CP_A}{CP_B} = \frac{2020}{1800} \]

To simplify this ratio, we can divide both numbers by 20:
\[ \text{Ratio} = \frac{101}{90} \]

### Final Answer
The ratio of the cost price of the articles of A to that of B is \( 101:90 \).

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