Question : Find the fourth proportion of the numbers $\frac{1}{3}{rd}$ of 15, $\frac{4}{5}{th}$ of 25, $\frac{3}{7}{th}$ of 35:

Option 1: 65

Option 2: 55

Option 3: 60

Option 4: 50

Question : What is the value of $x$?
$\frac{3}{2}× \frac{7}{3} ÷ \frac{7}{6}+\frac{1}{4}=\frac{1}{x}$

Option 1: $\frac{7}{12}$

Option 2: $\frac{4}{13}$

Option 3: $\frac{13}{4}$

Option 4: $\frac{6}{7}$

Question : The value of $2 \frac{3}{5} \div\left[2 \frac{1}{3} \div\left\{4 \frac{1}{3}-\left(2 \frac{1}{2}+\frac{2}{3}\right)\right\}\right]$ is equal to:

Option 1: $1 \frac{3}{10}$

Option 2: $2 \frac{7}{10}$

Option 3: $2 \frac{3}{7}$

Option 4: $1 \frac{3}{7}$

Question : If $\frac{x}{y}=\frac{4}{5}$, then the value of $(\frac{4}{7}+\frac{2y–x}{2y+x})$ is:

Option 1: $\frac{3}{7}$

Option 2: $1\frac{1}{7}$

Option 3: $1$

Option 4: $2$

Question : If $x+\frac{2}{x}=1$, then the value of $\frac{x^2+7x+2}{x^2+13x+2}$ is:

Option 1: $\frac{5}{7}$

Option 2: $\frac{3}{7}$

Option 3: $\frac{4}{7}$

Option 4: $\frac{2}{7}$