Multiple choice

By selling a product for Rs. $100$ how much profit was earned? (I) $20\%$ profit would have been earned if it had been sold for Rs. $90$. (II) The profit was one-third of the cost price

  1. Statement (I) ALONE is sufficient, but statement (II) B alone is not sufficient

  2. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

  4. EACH statement ALONE is sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I: If selling at 90 gives 20% profit, then 1.2 * CP = 90, so CP = 75. Selling at 100 gives 25 profit, which is known. Statement II: Profit = 1/3 * CP. Selling Price = CP + 1/3 * CP = 4/3 * CP. 100 = 4/3 * CP, so CP = 75, profit = 25. Both are sufficient independently.

AI explanation

Statement I allows you to find the cost price directly using the formula Cost Price equals 90 divided by 1.20, which gives a cost price of 75, so the profit for a 100 selling price is 25. Statement II provides a direct equation where Profit equals Cost Price divided by 3, meaning the Selling Price of 100 equals Cost Price plus Cost Price divided by 3, so Cost Price is 75 and the profit is 25. Each statement independently provides enough data to calculate the profit.

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