Question : A lady sold an article for INR 960 at some profit. Had she sold it for INR 800, then there would have been a loss equal to $\frac{1}{3}$rd of the initial profit. What was the profit percentage of the article?
Option 1: $\frac{150}{7} \%$
Option 2: $\frac{50}{7} \%$
Option 3: $\frac{10}{7} \%$
Option 4: $\frac{100}{7} \%$
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Correct Answer: $\frac{100}{7} \%$
Solution :
Let the cost price of the article be $x$.
According to the question,
⇒ $(x - 800) = \frac{1}{3}\times (960 - x)$
⇒ $3(x - 800) = 960 - x$
⇒ $3x - 2400 = 960 - x$
⇒ $3x + x = 960 + 2400$
⇒ $4x = 3360$
⇒ $x = \frac{3360}{4}$
⇒ $x = 840$
So, profit = 960 – 840 = 120
Thus, profit percentage = $\frac{\text{profit}}{\text{cost price}}\times 100$
= $\frac{120}{840}\times 100$
= $\frac{100}{7}\%$
Hence, the correct answer is $\frac{100}{7}\%$.
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