Three numbers are in the ratio of $3:2:5$ and the sum of their squares is $1862$. The smallest of these numbers is:

The ratio between the present ages of Indira and Lizzy is $3:8$,respectively. After $8 \text{ yr}$,Indira's age will be $20 \text{ yr}$. What was Lizzy's age $5 \text{ yr}$ ago (in $\text{yr}$)?

If $A: B = 8: 15$,$B: C = 5: 8$,and $C: D = 4: 5$,then $A: D$ is equal to:

If $m : n = 3 : 2,$ then $(4m + 5n) : (4m - 5n)$ is equal to:

When $x$ is added to each term of $7: 13$,the ratio becomes $2: 3$. The value of $x$ is

$A$ certain amount was to be distributed among $A$,$B$,and $C$ in the ratio $2:3:4$,but was erroneously distributed in the ratio $7:2:5$. As a result of this,$B$ received ₹ $40$ less. What is the actual amount (in ₹)?