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# A seller uses 840 gm in place of 1 kg to sell his goods. If he sells the goods 4% less than the cost price of 1 kg, what is the actual profit/ loss% for the seller.

Last updated date: 20th Jun 2024
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Hint: We start solving problems by assuming a cost price for 1 kg of goods. We use this cost price to find the cost price of 840gm of goods. Now, we apply a discount on the cost price of 1 kg goods. Now, this new cost price for 1 kg goods will be the new selling price for 840 gm goods. So, we subtract the cost price of 840 gm goods from the new selling price of 840 gm goods to get profit/loss. Once we find the profit/loss we convert them to percentage.

Given that the seller uses 840 grams in place of 1 kg to sell his goods. He gives 4% discount to the customers for 1 kg of his goods. We need to find the percentage of profit/ loss incurred to the seller.
Let us assume the cost price of 1 kg of goods is Rs. X $\left( X > 0 \right)$. This makes the actual cost price of 840 gm goods as Rs. 0.84X.
Seller is giving a 4% discount on 1kg goods.
So, the new cost price of 1 kg of goods is “96% of Rs. X”.
New cost price of 1 kg of goods is $\dfrac{96}{100}\times X$.
New cost price of 1 kg of goods is Rs. 0.96X.
But he is selling 840 gm by telling that the goods are of 1 kg.
Now, we check the difference between selling price and cost price.
Selling price – cost price = Rs. 0.96X – Rs.0.84X.
Selling price – cost price = Rs. 0.12X.
Here we got the value of selling price – cost price >0, which means that the seller is making the profit.
We know that profit = selling price – cost price.
So, selling is making profit Rs. 0.12X. Now, we find the percentage of profit.
We know that the percentage of profit is defined as $\text{ }\!\!\%\!\!\text{ profit=}\dfrac{\text{profit}}{\text{cost price}}\text{ }\!\!\times\!\!\text{ 100}$.
$\%profit=\dfrac{0.12X}{0.84X}\times 100$.
$\%profit=\dfrac{100}{7}\%$.

∴ The percentage of profit made by seller is $\dfrac{100}{7}\%$.

Note: We should not take the value Rs. 0.96X as the cost price for 1 kg of goods as he is selling only 840 gm. We always find % profit/loss with respect to the actual cost price which is Rs.0.84X. Mistakes may happen by multiplying 4% directly to the cost price of 840gms. We should remember that he is not telling customers that he is selling 840 gm instead of 1 kg.