Solution

Let cost price be Rs.100a Marked price = 100a×160/100=Rs.160a From (i) Profit percent when he allows X% discount = 28% So, selling price = 100a×128/100=Rs.128a Value of X = (160a-128a)/160a×100=20% When he allows 1.5X% discount so, discount percentage = 1.5×20=30% New selling price = 160a×70/100=Rs.112a New profit percentage = (112a-100a)/100a×100=12% So, (i) is possible to fill the both respective fillers  From (ii) Profit percent when he allows X% discount = 36% So, selling price = 100a×136/100=Rs.136a Value of X = (160a-136a)/160a×100=15% When he allows 1.5X% discount so, discount percentage = 1.5×15=22.5% New selling price = 160a×((100-22.5))/100=Rs.124a New profit percentage = (124a-100a)/100a×100=24% So, (ii) is possible to fill the both respective fillers  From (iii) Profit percent when he allows X% discount = 47.2% So, selling price = 100a×147.2/100=Rs.147.2a Value of X = (160a-147.2a)/160a×100=8% When he allows 1.5X% discount so, discount percentage = 1.5×8=12% New selling price = 160a×((100-12))/100=Rs.140.8a New profit percentage = (140.8a-100a)/100a×100=40.8% So, (iii)  can’t fill both respective fillers  So, both (i) & (ii)