Multiple choice

Smith buys an article marked at Rs. $2,200.$ The rate of Sales Tax is $12\%$. He asks the shopkeeper to reduce the price of the article to such an extent that he does not have to pay anything more than Rs. $2,240$ including Sales Tax. Calculate the reduction, as percent, needed in the marked price of the article.

  1. $9\displaystyle\frac{2}{13}$%
  2. $9\displaystyle\frac{1}{11}$%
  3. $7\displaystyle\frac{1}{9}$%

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let marked price be M. Selling price including 12% tax = 1.12 * (M - reduction). 1.12 * (M - R) = 2240. M = 2200. 1.12 * (2200 - R) = 2240 => 2200 - R = 2000 => R = 200. Reduction percent = (200/2200) * 100 = 100/11 = 9 1/11%.

AI explanation

Smith wants the final price including the 12 percent sales tax to be 2240, so the new reduced price of the article is 2240 divided by 1.12, which is 2000. The original marked price is 2200, so the required reduction in price is 2200 minus 2000, which is 200. The reduction as a percentage of the marked price is 200 divided by 2200 multiplied by 100, resulting in 9 and one-eleventh percent.

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