Question : If the numerator of a fraction is increased by 140% and the denominator of the fraction is decreased by 20%, the resultant fraction is $\frac{12}{7}$. Find the original fraction.
Option 1: $\frac{4}{9}$
Option 2: $\frac{4}{7}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{8}{9}$
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Correct Answer: $\frac{4}{7}$
Solution : Let $\frac{x}{y}$ be the original fraction. The fraction's numerator is increased by 140% and the denominator is decreased by 20%. $\frac{x+1.4x}{y-0.2y} = \frac{12}{7}$ ⇒$\frac{2.4x}{0.8y} = \frac{12}{7}$ ⇒$\frac{3x}{y} = \frac{12}{7}$ ⇒$\frac{x}{y} = \frac{12}{7\times 3}$ ⇒$\frac{x}{y} = \frac{4}{7}$ Hence, the correct answer is $\frac{4}{7}$.
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Question : A number is first increased by 16% and then increased by 20%. The number so obtained has now decreased by 40%. The net decrease percentage in the original number is:
Option 1: $16 \frac{12}{25}$%
Option 2: $15 \frac{9}{25}$%
Option 3: $11 \frac{13}{25}$%
Option 4: $13 \frac{7}{25}$%
Question : The arrangement of the fractions $\frac{4}{3}, -\frac{2}{9}, -\frac{7}{8}, \frac{5}{12}$ in ascending order is _____.
Option 1: $–\frac{7}{8}, –\frac{2}{9}, \frac{5}{12}, \frac{4}{3}$
Option 2: $–\frac{7}{8}, –\frac{2}{9}, \frac{4}{3}, \frac{5}{12}$
Option 3: $–\frac{2}{9}, –\frac{7}{8}, \frac{5}{12}, \frac{4}{3}$
Option 4: $–\frac{2}{9}, –\frac{7}{8}, \frac{4}{3}, \frac{5}{12}$
Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.
Option 1: $5\frac{1}{9}$
Option 2: $4\frac{5}{6}$
Option 3: $7\frac{1}{9}$
Option 4: $9\frac{1}{9}$
Question : If a number is increased by 25% and the resulting number is decreased by 25%, then the percentage increase or decrease finally is:
Option 1: no change
Option 2: decreased by $6\tfrac{1}{4}$%
Option 3: increased by $6\tfrac{1}{4}$%
Option 4: increased by $6$%
Question : A number is first decreased by 20%. The decreased number is then increased by 20%. The resulting number is less than the original number by 20. Then the original number is:
Option 1: 200
Option 2: 400
Option 3: 500
Option 4: 600
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