Explanation
To determine the overall percentage gain or loss in the transaction, we first need to establish the cost prices of the two chairs and then calculate the net gain or loss.
**Chair 1:**
- Selling Price (SP) = Rs. 1,200
- Gain = 20%
LetC_1 be the cost price of the first chair.
Since he gained 20%, we use the formula for the selling price:
SP = C_1 + (0.20 times C_1
1,200 = 1.20 times C_1
C_1 = frac{1,200}{1.20}
C_1 = 1,000
So, the cost price of the first chair is Rs. 1,000.
**Chair 2:**
- Selling Price (SP) = Rs. 1,200
- Loss = 20%
Let ( C_2 ) be the cost price of the second chair.
Since he lost 20%, we use the formula for selling price:
SP = C_2 - (0.20 times C_2)
1,200 = 0.80 times C_2
C_2 = frac{1,200}{0.80}
C_2 = 1,500
So, the cost price of the second chair is Rs. 1,500.
**Total Cost Price and Total Selling Price:**
- Total Cost Price = C_1 + C_2 = 1,000 + 1,500 = 2,500
- Total Selling Price = Rs. 1,200 + Rs. 1,200 = Rs. 2,400
**Net Loss:**
text{Net Loss} = text{Total Cost Price} - text{Total Selling Price}
ext{Net Loss} = 2,500 - 2,400 = 100
**Percentage Loss:**
text{Percentage Loss} = left( frac{text{Net Loss}}{text{Total Cost Price}} right) times 100
text{Percentage Loss} = left( frac{100}{2,500} right) times 100
text{Percentage Loss} = 4%
