Yash scored $40$ marks in a test, getting $3$ marks for each right answer and losing $1$ marks for each wrong answer. If $4$ marks had been awarded for each correct answer and $2$ marks been deducted for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

Form the pair of linear equation in the following problem and find its solution(if they exist) by any algebraic method:

Places $\mathrm{A}$ and $\mathrm{B}$ are $100\mathrm{}\mathrm{k}\mathrm{m}$ apart on a highway. One car starts from $\mathrm{A}$ and another from $\mathrm{B}$ at the same time. If the cars travel in the same direction at different speeds, they meet in $5$ hours. If they travel towards each other, they meet in $1$ hour. What are the speeds of the two cars?

Form the pair of linear equations in the following problem and find their solutions (if they exist) by any algebraic method:

 The area of a rectangle gets reduced by $9$ square units, if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units, the area increases by $67$ square units. Find the dimensions of the rectangle.

Solve the following pairs of equations by reducing them to a pair of linear equations:

$\frac{1}{2x}+\frac{1}{3y}=2; \frac{1}{3x}+\frac{1}{2y}=\frac{13}{6}$

Solve the following pairs of equations by reducing them to a pair of linear equations:

$$\begin{gathered} \left(\mathrm{ii}\right) \frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2 \\ \frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1 \end{gathered}$$

Solve the following pairs of equations by reducing them to a pair of linear equations.

$\frac{4}{x}+3y=14$

$\frac{3}{x}-4y=23$

Solve the following pairs of equations by reducing them to a pair of linear equations.

$\frac{5}{x-1}+\frac{1}{y-2}=2$

$\frac{6}{x-1}-\frac{3}{y-2}=1$

Solve the following pairs of equations by reducing them to a pair of linear equations.

$\frac{7x-2y}{xy}=5$

$\frac{8x+7y}{xy}=15$

Solve the following pairs of equations by reducing them to a pair of linear equations.

$6x+3y=6xy$

$2x+4y=5xy$