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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