Mukesh sells two shirts. The cost price of the first shirt is equal to the selling price of the second shirt. The first shirt is sold at a profit of 30% and the second shirt is sold at a loss of 30%. What is the ratio of the selling price of the first shirt to the cost price of the second shirt?

Options

A. `91: 100`
B. `100:91`
C. `31:50`
D. `50 : 31`

Answer

To solve the problem, let's denote the following:

- Let the cost price (CP) of the first shirt be \( CP_1 \).
- Let the selling price (SP) of the first shirt be \( SP_1 \).
- Let the cost price (CP) of the second shirt be \( CP_2 \).
- Let the selling price (SP) of the second shirt be \( SP_2 \).

According to the problem:

1. The first shirt is sold at a profit of 30%. Therefore, we can express the selling price of the first shirt as:
\[ SP_1 = CP_1 + 0.30 \times CP_1 = 1.30 \times CP_1 \]

2. The second shirt is sold at a loss of 30%. Therefore, we can express the selling price of the second shirt as:
\[ SP_2 = CP_2 - 0.30 \times CP_2 = 0.70 \times CP_2 \]

3. The problem states that the cost price of the first shirt is equal to the selling price of the second shirt:
\[ CP_1 = SP_2 \]

Now, substituting the expression for \( SP_2 \):
\[ CP_1 = 0.70 \times CP_2 \]

Next, we need to find the ratio of the selling price of the first shirt to the cost price of the second shirt:
\[ \text{Ratio} = \frac{SP_1}{CP_2} \]

Substituting \( SP_1 \) and \( CP_2 \) in terms of \( CP_1 \):
1. From \( CP_1 = 0.70 \times CP_2 \), we can express \( CP_2 \) as:
\[ CP_2 = \frac{CP_1}{0.70} \]

2. Now substituting \( CP_2 \) into the ratio:
\[ \text{Ratio} = \frac{1.30 \times CP_1}{CP_2} = \frac{1.30 \times CP_1}{\frac{CP_1}{0.70}} = 1.30 \times 0.70 \]

3. Calculate the ratio:
\[ \text{Ratio} = 0.91 \]

Thus, the ratio of the selling price of the first shirt to the cost price of the second shirt is:
\[ \text{Ratio} = 1.3 : 1 \]