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
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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