On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$

The cost of $2\, kg$ of apples and $1\, kg$ of grapes on a day was found to be ₹ $160$. After a month,the cost of $4\, kg$ of apples and $2\, kg$ of grapes is ₹ $300$. Represent the situation algebraically and geometrically.

Places $A$ and $B$ are $100 \ km$ apart on a highway. One car starts from $A$ and another from $B$ at the same time. If the cars travel in the same direction at different speeds,they meet in $5 \ hours$. If they travel towards each other,they meet in $1 \ hour$. What are the speeds of the two cars?

Which of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$x - 3y - 7 = 0$
$3x - 3y - 15 = 0$

Solve the following pair of equations by reducing them to a pair of linear equations:
$6x + 3y = 6xy$
$2x + 4y = 5xy$

$A$ train covered a certain distance at a uniform speed. If the train would have been $10\, km/h$ faster,it would have taken $2\, hours$ less than the scheduled time. And,if the train were slower by $10\, km/h$,it would have taken $3\, hours$ more than the scheduled time. Find the distance covered by the train. (in $, km$)