In a two-digit number, the digit at the unit's place is $x$ and the digit at the ten's place is $2x$. Then, the number is..........

Solve the following pair of equations by the cross-multiplication method:
$\frac{x}{a} + \frac{y}{b} = a + b$
$\frac{x}{a^2} + \frac{y}{b^2} = 2$

The cost of $2\,kg$ of apples and $1\,kg$ of grapes on a day was found to be Rs. $160$. After a month,the cost of $4\,kg$ of apples and $2\,kg$ of grapes is Rs. $300$. Represent this situation as a pair of linear equations in two variables.

An employee invests ₹ $x$ at the rate of $5 \%$ and invests ₹ $y$ at the rate of $7 \%$,then he gets ₹ $310$ as yearly interest. Symbolically it is written as ..........

Solve the following pair of equations: $(a \neq 0, b \neq 0)$
$\frac{5}{a} + \frac{3}{2b} = 1$
$\frac{1}{2a} - \frac{3}{b} = 1$

$y$ years ago,the sum of the ages of five friends was $x$ years,then the sum of the present ages of them is $\ldots \ldots \ldots \ldots$ years.