To solve the problem step by step, we will follow the given information and perform the necessary calculations.
### Step 1: Understand the Problem
Reshma buys two articles A and B for a total of ₹1,734. She sells article A at a loss of 16% and article B at a gain of 20%. The selling price of both articles is the same, and we know that article A is sold for ₹1,147.50.
### Step 2: Calculate the Cost Price of Article A
Since article A is sold at a loss of 16%, we can express the selling price (SP) in terms of the cost price (CP):
\[
SP_A = CP_A - (16\% \text{ of } CP_A) = CP_A \times (1 - 0.16) = CP_A \times 0.84
\]
Given that \(SP_A = ₹1,147.50\), we can set up the equation:
\[
1,147.50 = CP_A \times 0.84
\]
To find \(CP_A\), we rearrange the equation:
\[
CP_A = \frac{1,147.50}{0.84}
\]
### Step 3: Calculate the Cost Price of Article A
Now we perform the calculation:
\[
CP_A = \frac{1,147.50}{0.84} = 1,365.48
\]
### Step 4: Calculate the Cost Price of Article B
Since the total cost price of both articles A and B is ₹1,734, we can find the cost price of article B:
\[
CP_B = 1,734 - CP_A
\]
Substituting the value of \(CP_A\):
\[
CP_B = 1,734 - 1,365.48 = 368.52
\]
### Step 5: Calculate Selling Price of Article B
Since article B is sold at a gain of 20%, we can express the selling price in terms of the cost price:
\[
SP_B = CP_B + (20\% \text{ of } CP_B) = CP_B \times (1 + 0.20) = CP_B \times 1.20
\]
Substituting the value of \(CP_B\):
\[
SP_B = 368.52 \times 1.20 = 442.224
\]
### Step 6: Calculate the Gain Percentage on Article A
The gain on article A can be calculated as:
\[
\text{Gain} = SP_A - CP_A = 1,147.50 - 1,365.48 = -217.98
\]
Since there is a loss, we will calculate the loss percentage instead:
\[
\text{Loss Percentage} = \left(\frac{\text{Loss}}{CP_A}\right) \times 100 = \left(\frac{217.98}{1,365.48}\right) \times 100
\]
Calculating this gives:
\[
\text{Loss Percentage} = 15.98\%
\]
### Final Answer
The gain percent on article A is actually a loss of approximately 16%.
