An article is marked x% (0 < x < 40) above its cost price. It is sold by giving x/2% discount on its marked price. If there is a profit of 10(1/2)%, then what is the value of x?
Marked Price (MP): M = C (1 + x/100) Selling Price (SP) with discount%: SP = M (1 - x/200) Profit of 10%: SP = C ×1.105 ATQ- C × 1.105 = C (1 + x/100) (1 - x/200) 1.105 = (1 + x/100) (1 - x/200) 1.105 = 1 + x/200 - (x 2)/20000 0.105 = x/200 - (x2)/20000 2100= 100x - x 2 x2 - 100x + 2100 = 0 x2 - 70x-30x + 2100 =0 x(x-70)-30(x-70) =0 x=30 Since x must be less than 40: x=30 So, the value of x is 30.
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