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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