The ratio of two numbers is $10: 7$ and their difference is $105$. The sum of these numbers is

The price of a diamond is directly proportional to the square of its weight. $A$ man accidentally broke the diamond into three pieces in the ratio of $3:5:7$ and thus lost ₹ $42600$. What was the original price (in ₹) of the diamond?

The number of students in three classes are in the ratio $2:3:4$. If $12$ students are increased in each class,this ratio changes to $8:11:14$. The total number of students in the three classes in the beginning was:

₹ $73,689$ are divided between $A$ and $B$ in the ratio $4:7$. What is the difference between thrice the share of $A$ and twice the share of $B$? (In ₹)

If $50$ fewer candidates had applied and $25$ fewer had been selected,the ratio of selected to unselected candidates would have been $9:4$. How many candidates had applied if the initial ratio of selected to unselected candidates was $2:1$?

Calculate the fourth proportional to the numbers $286, 78, 1342$.