Cost price of an article is X. The article is marked up by Y% and sold while offering a discount of 25%. The profit earned is (Y + 20). When the same article is marked up by (Y + 5)% and sold while offering a discount of 25%, the profit earned is (Y + 65). Which of the following statement is correct?
CP = X MP = (X + XY/100) SP = (X + XY/100) x 75/100 Profit = (Y + 20) We know that, Profit = SP – CP Profit + CP = SP (X + XY/100) x (3/4) = X + Y + 20 ----------(1) Similarly, when the same article is marked up by (Y + 5)% and the profit earned is (Y + 65). We will get: {X + X(Y + 5)/100} x (3/4) = X + Y + 65 ----(2) Subtracting equation (1) by (2), we get {X + X(Y + 5)/100} x (3/4) - (X + XY/100) x (3/4) = (X + Y + 65) – (X + Y + 20) 3/4 { (X + XY + 5X – X – XY)/100} = 45 3/4 x 5X/100 = 45 X = 1200 Y = 40 Putting the value of X and Y in 0.5X = 15Y => 0.5 x 1200 = 15 x 40 => 600 = 600 Therefore, statement I is true.
