The marked price of an article in two different shops P and Q is Rs 1200 and Rs X respectively. In shop P the article is available at two successive discounts of d% and 25%, while in shop Q the article is available at two successive discounts of 10% and 20%. If the ratio of the selling price of an article at shop Q to the selling price of an article at shop P is X:800, then find which of the following statements is/are true.
(I) d2 is completely divisible by 24
(II) d is a multiple of both 12 and 3
(III) d% of 750 is equals to 270
Given, Selling price of the article at shop P = 1200 ×(100-d)/100 × 75/100. Selling price of the article at shop Q = X ×90/100 × 80/100 ATQ – (X ×(90/100) ×(80/100))/(1200 ×(100-d)/100 ×(75/100))= X/800 d = 36 From (I) d2= 362 = 1296 1296 is completely divisible by 24. From (II) d= 36 36 is multiple of both 12 and 3 From (II) d=36 (36/100)×750=270
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