A person X sells an article of Rs 100 with a loss of 10% to the person Y. Y sells it at a gain of 10% to another person Z. What is the price at which Y sold the article to Z?

Options

A. Rs 100
B. Rs 99
C. Rs 110
D. Rs 101

Answer

To solve the problem step by step, we will calculate the selling price of the article from person Y to person Z.

### Step 1: Calculate the cost price for person Y
Person X sells the article for Rs 100 with a loss of 10%.

To find the cost price (CP) for person Y, we can use the formula for loss:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} - \text{Loss} \]
Given that the loss is 10%, the selling price can be expressed as:
\[ \text{SP} = \text{CP} \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values:
\[ 100 = \text{CP} \times \left(1 - \frac{10}{100}\right) \]
\[ 100 = \text{CP} \times 0.9 \]

Now, we can solve for CP:
\[ \text{CP} = \frac{100}{0.9} \]
\[ \text{CP} = 111.11 \]

### Step 2: Calculate the selling price for person Z
Now, person Y sells the article at a gain of 10%.

To find the selling price (SP) for person Z, we can use the formula for profit:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
The profit can be calculated as:
\[ \text{Profit} = \text{CP} \times \frac{\text{Profit \%}}{100} \]
Substituting the values:
\[ \text{Profit} = 111.11 \times \frac{10}{100} \]
\[ \text{Profit} = 11.11 \]

Now, we can find the selling price:
\[ \text{SP} = 111.11 + 11.11 \]
\[ \text{SP} = 122.22 \]

### Conclusion
Thus, person Y sold the article to person Z for Rs 122.22.