The number that must be added to each of the numbers $8, 21, 13$ and $31$ to make the ratio of the first two numbers equal to the ratio of the last two numbers is:

If $x: y = 2: 1,$ then $(x^{2} - y^{2}) : (x^{2} + y^{2})$ is

In a school,there were $1554$ students and the ratio of the number of boys to girls was $4:3$. After a few days,$30$ girls joined the school but some boys left; as a result,the ratio of boys to girls became $7:6$. The number of boys who left the school is:

How many one-rupee coins,$50$-paise coins,and $25$-paise coins,whose numbers are in the ratio $5:7:12$,are together worth $₹ 115$?

If $(x+y):(x-y)=11:1$,find the value of $\frac{(5x+3y)}{(x-2y)}$.

$A$ bag contains $10$-paise and $25$-paise coins in the ratio of $17:6$. If the total money in the bag is $Rs. 112$,the number of $10$-paise coins is: