Maheep travels $600 km$ partly by train and partly by car. He takes $8$ hours to cover the whole distance if he travels $120 km$ by train and rest by car. But he takes $20$ minutes longer if he travels $200 km$ by train and the rest by car. Find the speed of train and car.

Two towns $A$ and $B$ are $120 km$ apart on the highway. One car starts from $A$ and the other from $B$ at the same time at different speeds. If the car travels in the same direction, the car meets in $4$ hours. But when they travel towards each other, they meet in $1$ hour. Find their speeds.

Solve the pair of equations given below:

$\frac{x}{3}+\frac{y}{2}=4, \frac{{\displaystyle x}}{{\displaystyle 2}}+\frac{{\displaystyle y}}{{\displaystyle 4}}=4$

Solve the pair of equations given below:

$97x-78y=310, 78x-97y=215$

Solve the pair of equations given below:

$\frac{{\displaystyle 14}}{{\displaystyle x}}+\frac{{\displaystyle 3}}{{\displaystyle y}}=5, \frac{{\displaystyle 21}}{{\displaystyle x}}-\frac{{\displaystyle 8}}{{\displaystyle y}}=-5$

Solve the pair of equations given below:

$\frac{12}{x+y}-\frac{4}{x-y}=1, \frac{28}{x+y}-\frac{4}{x-y}=5$

Amrita came first in $x$ races and second in $y$ races. A score of $5$ points is given for coming first and $3$ points for the second place in the race. She scored $34$ points but if the number of games in which she came first and second were interchanged she would have scored $4$ points less. Find $x$ and $y$.

For a school concert, $210$ tickets are sold. Of the tickets, some were for adults and other for students. The total money collected is $₹4300$. If adult ticket costs $₹25$ each and student ticket costs $₹15$ each, find the number of tickets sold of each kind.

An instructor scored a student's test of $50$ questions by giving $2$ marks for a right answer and $-1$ for a wrong answer. If the score is $76$, find out the number of right answers.