Two circles touch internally. The sum of their areas is $116\, \pi \, cm^2$ and the distance between their centers is $6 \, cm$. Then,the radii of the circles are?

$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?

The length and breadth of a rectangular field are in the ratio $5: 3.$ If the cost of cultivating the field at $25$ $paise$ per square metre is ₹ $6000,$ then find the dimensions of the field.

In $\Delta ABC,$ a line through $A$ cuts the side $BC$ at $D$ such that $BD : DC = 4 : 5.$ If the area of $\Delta ABD = 60 \, cm^2,$ then the area of $\Delta ADC$ is......$cm^2$.

$A$ room is $7 \text{ m}$ long and $5 \text{ m}$ broad. The doors and windows occupy $5 \text{ m}^2$. The cost of papering the remaining part of the walls with paper $75 \text{ cm}$ wide,at ₹ $4.20$ per piece of $13 \text{ m}$,is ₹ $39.20$. Find the height of the room (in $\text{m}$).

Each side of a rhombus is $26 \ cm$ and one of its diagonals is $48 \ cm$ long. The area of the rhombus is (in $cm^2$)