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
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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