Multiple choice

A person sells an article for Rs.75 and gains as much per cent as the cost price of the article. What is the cost price of the article ?

  1. Rs. 40

  2. Rs. 50

  3. Rs. 60

  4. Rs. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let CP = x. Gain % = x%. Selling Price = CP + Gain = x + (x/100)*x = 75. x^2 + 100x - 7500 = 0. (x + 150)(x - 50) = 0. Since CP > 0, x = 50.

AI explanation

Let the cost price be Rs.x, meaning the gain percentage is also x%. Using the profit formula, selling price equals cost price plus profit, so 75 equals x plus x% of x, which is x plus 0.01x squared. Rearranging this gives the quadratic equation 0.01x squared plus x minus 75 equals 0, or x squared plus 100x minus 7500 equals 0. Solving this yields factors of (x plus 150) and (x minus 50), so the valid cost price is Rs.50.

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