Question : Anil sold an article at a loss of 15%. Had he sold it for Rs. 84 more, he would have gained 13%. At what price should he have sold it to gain 20%?
Option 1: Rs. 360
Option 2: Rs. 375
Option 3: Rs. 350
Option 4: Rs. 300
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Correct Answer: Rs. 360
Solution : Let the cost price of the article as C. Anil sold the article at a loss of 15%, so the selling price (S1) was 85% of the cost price, ⇒ S1 = 0.85C If Anil had sold it for Rs. 84 more, he would have gained 13%, so the selling price (S2) would have been 113% of the cost price, ⇒ S2 = 1.13C But we also know that S2 is Rs. 84 more than S1: ⇒ S2 = S1 + 84 Substituting the expressions for S1 and S2 from the first two equations into this equation gives, ⇒ 1.13C = 0.85C + 84 Solving this equation for C gives the cost price of the article. ⇒ C = $\frac{84}{1.13 - 0.85}$ = 300 To gain 20%, Anil should have sold the article for 120% of the cost price. ⇒ S = 1.2C = 1.2 × 300 = 360 Hence, the correct answer is Rs. 360.
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