Question : A radio dealer sold a radio at a loss of 2.5%. Had he sold it for Rs. 100 more, he would have gained $7\frac{1}{2}$%. In order to gain $12\frac{1}{2}$% he should sell it for_______
Option 1: Rs. 1080
Option 2: Rs. 1125
Option 3: Rs. 850
Option 4: Rs. 925
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Correct Answer: Rs. 1125
Solution : Here, the cost price is denoted by CP and SP denotes the selling price. If the CP of the radio is Rs. $x$, then Difference in the profits = Difference in respective selling price ⇒ 2.5% of $x$ + 7.5% of $x$ = Rs. 100 ⇒ 10% of $x$ = Rs. 100 ⇒ $x$ = Rs. 1000 For a gain of $12\frac{1}{2}$% SP = CP$(\frac{100+Profit\%}{100})$ ⇒ SP = 1000$(\frac{100+\frac{25}{2}}{100})$ ⇒ SP = 1000$(\frac{225}{200})$ ⇒ SP = Rs. 1125 Hence, the correct answer is Rs. 1125.
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