If the sum of two numbers is $20$ and their difference is $8,$ then the larger number is ...........

The sum of the digits of a two-digit number is $9$ and the difference is $1$. The number is ............

The denominator of a fraction is $6$ more than the numerator. If $1$ is added to the numerator and $3$ is subtracted from the denominator,the fraction becomes $\frac{3}{4}$. Find the fraction.

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?

The solution set of a pair of equations $x=4$ and $y=5$ is $\ldots \ldots \ldots \ldots$

Do the equations $4x + 3y - 1 = 5$ and $12x + 9y = 15$ represent a pair of coincident lines? Justify your answer.