Exercise

If $0.142857142857\dots$ express in the form of $\frac{m}{n}$, then the value of $(2 m+n)$ is

Five years ago, Anu was thrice old as Sonu. After ten years, Anu will be twice old as Sonu. How old are Anu and Sonu?

A three wheeler scooter charges $\mathrm{₹}10$ for the first kilometer and $\mathrm{₹}4.50$ each for every subsequent kilometer. Taking the distance covered as $x \mathrm{km}$ and total fare as $\mathrm{₹}\mathrm{y}$. Write a linear equation for this information and draw the graph.

Two men start from points $A$ and $B$ respectively, $50 \mathrm{k}\mathrm{m}$ apart. One walks from $A$ to $B$ at $x \mathrm{k}\mathrm{m}/\mathrm{h}\mathrm{r}$ and another walks from $B$ to $A$ at $y \mathrm{k}\mathrm{m}/\mathrm{h}\mathrm{r}$. They meet each other after $5$ hours. Write a linear equation for this information and draw its graph.

A fraction becomes $\frac{9}{11}$, if $2$ is added to both the numerator and the denominator. The numerator and denominator of the fraction are $x$ and $y$ respectively. Write a linear equation for this information and draw the graph.

Give the geometric representation of the following equation (i) in one variable. (ii) in two variables.. And also identify the line parallel to which axis.

$-4-2x=x+5$

Angles of a quadrilateral are $5x,4x,6y$ and $3y$. Write a linear equation which satisfies this data. Draw the graph for the same.

If $a{x}^{-2a^2+3}+b{y}^{b^2-3}+2y^{b^2-3}+x^{-2a^2+3}=4$ is a linear equation in $x$ and $y$ then the value of $a+b$ is