Question

A dealer sold two types of goods for 10,000 each. On one of them, he lost 20% and on the other, he gained 20% find his gain or loss per cent on the entire transaction.
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Answer 1

The seller incurs a loss of 4% overall on both goods.

• Two goods are sold at Rs. 10000 each.

• On one the seller gains 20% and on one 20% .
• We have to find the overall gain or loss percentage.
• Let us assume the cost price of first be $x_1$ and other be $x_2$.
• We have to calculate the profit and loss on the goods.
• Profit percentage = $\frac{10000-x_1}{x_1}$ × 100 = 20

$10000-x_1 = 0.20x_1$

10000 = $1.2x_1$

$x_1$ = 10000/1.2 = 8333.33 Rs.

• Therefore cost price of the product where the seller gains 20% is Rs. 8333.33.
• Loss percentage = $\frac{x_2-10000}{x_2}$ × 100 = 20

$x_2-10000$  = $0.2x_2$

$0.8x_2$  = 10000

$x_2$ = Rs. 12500

• Therefore cost price of the product where the seller loses 20% is Rs. 12500.
• Now we have to calculate the net profit or loss percentage, we find the total cost price of two goods,
• Total cost price = 8333.33 + 12500 = 20833.33 Rs.

• Now ,Profit on article 1 - Loss on article 2 = Net gain

(10000-8333.33) - (12500-10000) = Net gain

Net gain = 1666.67 - 2500 = -833.33

• Therefore the seller gains a loss of 833.33 Rs. total on both goods.

• Now net loss percentage = $\frac{Net \ loss}{total \ cost \ price}$ × 100  

Net loss percentage = $\frac{833.33}{20833.33}$ × 100 = 4%