Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.

By Ritesh|Updated : November 14th, 2022

(a) 15%

(b) 25%

(c) 35%

(d) 45%

Here x is 25%. According to the question we can write as:

SP of trader A = 1000 (1 + x/100) = 1000 + 10x

His profit will be:

Profit of trader A = 10x

According to the question we can write as:

MP of trader B = 2000 (1 + 2x/100) = 2000 + 40x

SP of trader B = 2000 (1 + 2x/100) (1 - x/100)

In simplification we get the:

= 2000 (1 + x/100 - 2x2/1002)

= 2000 + 20x + 0.4x2

Now consider,

Profit of trader B = 0.4x2 + 20x

Therefore both make the same profit:

10x = -0.4x2 + 20x

On rearranging:

0.4x2 = 10x

0.4x = 10

x = 25

Therefore the profit will be:

x = 25%

Formula to Calculate Market Prices for Goods

Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every good. We can determine the profit made or loss suffered for a certain product based on the values of these prices.

Profit is the money made when a thing is sold for more than it costs to produce.

Loss: The sum that the seller experiences as a result of selling the item for less than its cost is indicated.

Cost price: The price paid to purchase a good or service is referred to as the cost price. Denoted as CP as well.

Selling price: The selling price of a product is the price at which it is sold. Typically, it is identified as SP. also known as a sale price on occasion.

Summary:

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, find x.

Traders A and B buy two goods for Rs. 1000 and Rs. 2000 respectively. Trader A marks his goods up by x%, while trader B marks his goods up by 2x% and offers a discount of x%. If both make the same non-zero profit, x is 25%.

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