The total cost of $3$ pens and $4$ pencils is Rs. $23$ and the total cost of $2$ pens and $3$ pencils is Rs. $16$. Find the cost of a pen and a pencil each.

The pair of equations $x=a$ and $y=b$ graphically represents lines which are

In a competitive examination,one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$ marks. How many questions did she answer correctly?

Find the value of $k$ under the given condition for the following pair of linear equations: $2x - 3y = 1$ and $kx + 5y = 7$,such that the system has a unique solution.

The angles of a cyclic quadrilateral $ABCD$ are $\angle A = (6x + 10)^{\circ}$,$\angle B = (5x)^{\circ}$,$\angle C = (x + y)^{\circ}$,and $\angle D = (3y - 10)^{\circ}$. Find $x$ and $y$,and hence the values of the four angles.

Pathik travels $600 \, km$ to his home partly by train and partly by car. He takes $8$ hours if he travels $120 \, km$ by train and the rest by car. He takes $20$ minutes longer if he travels $200 \, km$ by train and the rest by car. Find the speed of the train and the car.