Three numbers are in the ratio $2:5:7$. The sum of the smallest and largest numbers equals the sum of the second number and $16$. What is the smallest number?

Three vessels having volumes in the ratio of $2: 3: 5$ are full of a mixture of water and milk. In the first vessel,the ratio of water and milk is $1: 3$,in the second $2: 3$,and in the third vessel,$2: 5$. If all the three vessels are poured into a large container,what is the resulting ratio of milk and water?

If $a-b : b-c : c-d = 1 : 2 : 3$,then what is the value of $(a+d) : c$?

$A$ certain sum was divided among $P$ and $Q$ in the ratio $5:6$. If $Q$'s share was ₹ $2400$,the total sum was (in ₹):

Find the third proportional to the numbers $4$ and $42$.

Divide ₹ $1,000$ among $P, Q,$ and $R$ such that $P$ gets $\frac{2}{3}$ of $Q$'s share and $R$ gets $\frac{5}{3}$ of $Q$'s share. What is the share of $Q$?