Question : The population of town B is 300% more than that of town A. For the next two years, the population of A increases by $x$% per year, and that of B decreases by the same percentage per year. After 2 years, if the population of A and B become equal, then the value of $x$ is ________.
Option 1: $30 \frac{2}{3}$
Option 2: $33 \frac{1}{3}$
Option 3: $40$
Option 4: $25$
Correct Answer: $33 \frac{1}{3}$
Solution : Given : The population of town B is 300% more than that of town A. Let the population of town A be 100. Then, the population of town B = 400 According to the question, $100 × \frac{100 + x}{100}×\frac{100 + x}{100} = 400 × \frac{100 -x}{100} ×\frac{100 -x}{100}$ $\Rightarrow (100\ +\ x)^2\ =\ 4(100\ -\ x)^2$ $\Rightarrow \frac{100\ +\ x}{100\ -\ x}\ =\ \frac{2}{1}$ $\Rightarrow (100+x) =(200-2x)$ $\therefore x = \frac{100}{3}\% = 33\tfrac{1}{3}\%$ Hence, the correct answer is $33\tfrac{1}{3}\%$.
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Question : The price of a car is first increased by 35% and after that, the price is decreased by 25% due to a reduction in sales. What is the net percentage change in the final price of the car?
Option 1: Decreases by $2 \frac{1}{5}$%
Option 2: Increases by $2 \frac{1}{3}$%
Option 3: Decreases by $1 \frac{3}{5}$%
Option 4: Increases by $1 \frac{1}{4}$%
Question : Find the HCF of $\frac{11}{25}, \frac{9}{20}, \frac{16}{15}$, and $\frac{10}{33}$.
Option 1: $\frac{1}{3300}$
Option 2: $\frac{1}{330}$
Option 3: $\frac{1}{33}$
Option 4: $\frac{1}{300}$
Question : If 30% of Ravi’s income is equal to 40% of Suresh’s income, then 50% of Ravi’s income is equal to what percentage of Suresh’s income?
Option 1: $66 \frac{1}{3} \%$
Option 2: $33\frac{1}{3} \%$
Option 3: $33 \frac{2}{3} \%$
Option 4: $66 \frac{2}{3} \%$
Question : If $x\left(5-\frac{2}{x}\right)=\frac{5}{x}$, then the value of $x^2+\frac{1}{x^2}$ is:
Option 1: $\frac{54}{25}$
Option 2: $\frac{53}{28}$
Option 3: $\frac{53}{27}$
Option 4: $\frac{54}{23}$
Question : If the selling price of 318 articles is equal to the cost price of 212 articles, then what is the loss percentage?
Option 1: $20$
Option 2: $33\frac{1}{3}$
Option 4: $33\frac{2}{3}$
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