Multiple choice

The marked price of an article is Rs. 1,500. If two successive discounts, each of x%, on the marked price are equal to a single discount of Rs. 587.40, then what will be the selling price of the article if a single discount of x% is given on the marked price?

  1. Rs. 1,025

  2. Rs. 1,155

  3. Rs. 1,170

  4. Rs. 1,200

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Successive discounts of x% are equivalent to a single discount of 587.40 on 1500. 1500 * (1 - x/100)^2 = 1500 - 587.40 = 912.60. (1 - x/100)^2 = 0.6084. 1 - x/100 = 0.78, so x = 22. Selling price with single discount of 22% = 1500 * (1 - 0.22) = 1500 * 0.78 = 1170.

AI explanation

Using the successive discount formula, the total discount is x + x minus x times x divided by 100, which equals 2x minus x squared divided by 100. Since this discount equals 587.40 on a marked price of 1500, we have 2x minus x squared divided by 100 equals 39.16. Solving this gives x equals 22. The required selling price with a single 22% discount is 1500 times 0.78, which equals 1170.

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