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..........

Ankita travels $14 \,km$ to her home partly by rickshaw and partly by bus. She takes half an $hour$ if she travels $2 \,km$ by rickshaw and the remaining distance by bus. On the other hand,if she travels $4 \,km$ by rickshaw and the remaining distance by bus,she takes $9 \,minutes$ longer. Find the speed of the rickshaw and of the bus (in $km/h$).

If $3x + 5y = 8$ and $5x + 3y = 24$,then $x - y = \ldots$

The ratio of incomes of two persons is $9:7$ and the ratio of their expenditures is $4:3$. If each of them manages to save ₹ $2000$ per month,find their monthly incomes.

Devarshi got thrice the marks as obtained by Maharshi in the annual examination of mathematics of standard $10$. The sum of the marks obtained by them was $150$. Represent this situation as a pair of linear equations in two variables.

Naresh has double the money that Yogesh has. If Naresh gives Yogesh ₹ $20$,then both have equal money. The pair of equations obtained from this data is $\ldots \ldots \ldots \ldots .$