Question : A person bought an article and sold it at a loss of 10%. If he had bought it for 30% less price and sold it for INR 90 more, then he would have earned a profit of 35%. What is the cost price of the article?
Option 1: INR 2400
Option 2: INR 2000
Option 3: INR 2100
Option 4: INR 2200
Correct Answer: INR 2000
Solution :
Let the cost price of an article be $100x$.
Loss = 10% of cost price = $10x$
Selling price = cost price – loss = $100x-10x=90x$
New cost price = $100x - 30\%$ of $100x=100x-30x=70x$
Profit = 35% of cost price = $\frac{35}{100}×70x=24.5x$
New selling price = cost price + profit = $70x+24.5x=94.5x$
$94.5x = 90x + 90$
$⇒4.5x = 90$
$⇒x = \frac{90}{4.5} = 20$
$\therefore$ Cost price = 20 × 100 = INR 2000
Hence, the correct answer is INR 2000.
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