70% of the cost price of an article is equal to 50% of its selling price. The percentage of profit or loss on the cost price is
40% profit
This is a profit-and-loss problem that reduces to expressing the selling price in terms of the cost price and then comparing the two. Profit or loss is always measured against the cost price.
We are told that 70% of the Cost Price equals 50% of the Selling Price. Writing this as an equation: 0.7 times CP = 0.5 times SP. Solving for SP gives SP = (0.7 divided by 0.5) times CP = 1.4 CP.
Since the selling price (1.4 CP) is greater than the cost price, the seller makes a gain. The profit is SP minus CP = 1.4CP minus CP = 0.4 CP. Expressing this as a percentage of the cost price: profit % = (0.4CP divided by CP) times 100 = 40%.
So the transaction yields a 40% profit. The loss options can be ruled out immediately, because the selling price came out larger than the cost price, so there is no question of a loss. The 20% figures come from a miscalculation — for instance, wrongly writing SP = 1.2 CP by dividing incorrectly, or reversing the ratio to 0.5/0.7. Careful substitution confirms the answer is 40% profit.
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Important Questions from Profit and Loss
By selling an article for Rs. 2,200, a profit of 10% is earned. If the same article is sold for Rs. 2,600, then what will be the gain percentage?
By selling an article for Rs. 640, a person loses 15% of its selling price. At what price (in Rs.) should he sell it to gain 15% on its cost price?
The selling prices of articles A and B are the same. A is sold at a profit of 28 percent and B is sold at a loss of 24 percent. If the total selling price of the both articles is Rs. 48640, then what is the cost price of A and B, respectively ?
The cost price of an article is Rs. 2800. Profit as a percentage of selling price is 20 percent. What is the actual profit (in Rs.) ?
A trader bought 640 kg of rice. He sold a part of rice at 20% profit and the rest at 5% loss. He earned a profit of 15% in the entire transaction. What is the quantity (in kg) of rice that he sold at 5% loss?
