In a two-digit number,the digit at the unit's place is $3x$ and the digit at the ten's place is $2x$. Then,that number is $\ldots \ldots \ldots \ldots$

Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$	Part $II$
$1. x+2y=3, 2x+4y=5$	$a. \text{Solution set is a singleton set.}$
$2. 2x+3y=6, x+\frac{3}{2}y=3$	$b. \text{Solution set is an empty set.}$
$3. 3x-y=0, x-y+6=0$	$c. \text{Solution set is an infinite set.}$
	$d. \text{Solution set contains two members.}$

From the equation $2x + 3y = 8$,we get $y = \ldots$

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.

Four years ago,the sum of the ages of a mother and her two daughters was $x$ years. What will be the sum of their ages after two years?

For a pair of equations $13x - 7y = 19$ and $7x - 13y = 31$,find the value of $x + y$.