Multiple choice

A trader bought an article for Rs. $x$ and sold it for Rs. $52$, thereby making a profit of $(x-10)$ per cent on his outlay. Calculate the cost price.

  1. Rs. $60$
  2. Rs. $70$
  3. Rs. $80$
  4. Rs. $40$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

CP = x. Profit % = x - 10. SP = 52. SP = CP(1 + Profit%/100). 52 = x(1 + (x - 10)/100) = x((90 + x)/100). 5200 = 90x + x^2. x^2 + 90x - 5200 = 0. (x + 130)(x - 40) = 0. x = 40.

AI explanation

The profit percentage is given by the formula (profit divided by cost price) multiplied by 100. The profit is (52 minus x), so the equation is ((52 minus x) divided by x) multiplied by 100 equals (x minus 10). Solving 5200 minus 100x equals x squared minus 10x gives the quadratic equation x squared minus 90x plus 5200 equals 0. Factoring this equation gives (x minus 40)(x minus 130) equals 0, so the cost price is Rs. 40.

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