Multiple choice

An article is sold at 45/2% profit. If the cost price and selling price are increased by Rs. 40 and Rs. 35 respectively, then the profit on that article will be 15%. Find the cost of that article.

  1. Rs. 146 2/3

  2. Rs. 156 2/3

  3. Rs. 146 1/3

  4. Rs. 156 1/3

  5. None of these
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A Correct answer
Explanation

Let the cost price be x. The initial profit is 45/2% = 22.5%, so the selling price is 1.225x. The new cost price is x + 40 and the new selling price is 1.225x + 35. The new profit is 15%, so (1.225x + 35) / (x + 40) = 1.15. Solving this: 1.225x + 35 = 1.15x + 46, which gives 0.075x = 11. Thus, x = 11 / 0.075 = 146.666..., which is 146 2/3.

AI explanation

Using the formula for profit percentage, the initial selling price is the cost price multiplied by 1.225. When the cost price increases by Rs. 40 and the selling price increases by Rs. 35, the new profit is 15%, leading to the equation (SP + 35) = 1.15 * (CP + 40). Substituting SP with 1.225CP gives 1.225CP + 35 = 1.15CP + 46, which simplifies to 0.075CP = 11. Solving this yields the cost price as 11 divided by 0.075, which equals Rs. 146 2/3.

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