Multiple choice

An article is sold at a loss of $10\%$. Had it been sold for Rs. $9$ more there would have been a gain of $\displaystyle 12\frac{1}{2}$% on it. The cost price of the article is

  1. Rs. $40$
  2. Rs. $45$
  3. Rs. $50$
  4. Rs. $35$
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A Correct answer
Explanation

Let CP be x. Loss of 10% means SP = 0.9x. Gain of 12.5% (1/8) means SP = 1.125x. The difference is 0.225x = 9. x = 9 / 0.225 = 40.

AI explanation

By the percentage change method, the difference in selling prices equals the percentage difference applied to the cost price. The total percentage shift from a 10% loss to a 12.5% gain is 22.5%, so 22.5% of the cost price equals Rs. 9. Solving this gives 9 divided by 0.225, making the cost price Rs. 40.

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