Question : A businessman bought an article and sold it at a loss of 5%. If he had bought it for 10% less and sold it for Rs. 33 more, he would have had a profit of 30%. The cost price of the article is:
Option 1: Rs. 330
Option 2: Rs. 155
Option 3: Rs. 150
Option 4: Rs. 300
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Correct Answer: Rs. 150
Solution : Here CP denotes cost price and SP denotes selling price. Let CP = Rs. $x$ SP = $x(\frac{100-Loss\%}{100})$ ⇒ SP = $x(\frac{100-5}{100})$ ⇒ SP = $x(\frac{95}{100})$ New CP = $x-\frac{10}{100}x$ ⇒ New CP = $\frac{90}{100}x$ and new SP = $\frac{95}{100}x+33$ Profit = 30% New Profit = $\frac{95}{100}x+33 - \frac{90}{100}x$ ⇒ New Profit = $\frac{5}{100}x+33$ According to the question, $\frac{\frac{5}{100}x+33}{\frac{90}{100}x} \times 100 = 30$ ⇒ $\frac{5}{100}x+33 = 0.3(\frac{90}{100})x$ ⇒ $0.05x+33 = 0.3 \times 0.9x$ ⇒ $33 = 0.27x-0.05x$ ⇒ $33 = 0.22x$ ⇒ $x= Rs. 150$ Hence, the correct answer is Rs. 150.
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