Question : The percentage profit earned by selling an article for Rs. 2,000 is the same as the percentage loss incurred by selling the same article for Rs. 1,200. At what price should that article be sold to make a profit of 20%?
Option 1: 2,000
Option 2: 1,800
Option 3: 1,920
Option 4: 1,840
Correct Answer: 1,920
Solution :
Let the cost price be $x$.
Profit % earned by selling at Rs. 2000 = $\frac{2000-x} {x}\times 100$
Loss % earned by selling at Rs. 2000 = $\frac{x-1200} {x}\times 100$
So, $\frac{2000-x} {x}\times 100=\frac{x-1200} {x}\times 100$
⇒ $2000-x=x-1200$
⇒ $x=(\frac{2000+1200}{2})$
$\therefore x$ = Rs. 1600
To make a 20% profit,
The selling price will be = $1600×(\frac{100+20}{100})$ = Rs. 1920
Hence, the correct answer is 1,920.
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