If the sum of two numbers is $15$ and the subtraction is $1,$ then the smaller number of these two numbers is.........

Which of the following is a solution of the linear equation in two variables $x - 2y = 4$?

Are the following pair of linear equations consistent? Justify your answer.
$\frac{3}{5} x - y = \frac{1}{2}$
$\frac{1}{5} x - 3 y = \frac{1}{6}$

Susan invested a certain amount of money in two schemes $A$ and $B,$ which offer interest at the rate of $8 \%$ per annum and $9 \%$ per annum,respectively. She received $Rs.\, 1860$ as annual interest. However,had she interchanged the amount of investments in the two schemes,she would have received $Rs.\, 20$ more as annual interest. How much money did she invest in each scheme?

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.

If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$