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

₹ $1050$ are divided among $A, B$ and $C$ in such a way that the share of $A$ is $\frac{2}{5}$ of the combined share of $B$ and $C$. $A$ will get (in ₹):

If $A: B = 2: 5$,$B: C = 4: 3$,and $C: D = 2: 1$,what is the value of $A: C: D$?

Find the $4^{th}$ proportional to $4, 16$ and $7$.

$Rs. 2186$ is distributed among $A$,$B$,and $C$. If the money given to them is decreased by $Rs. 26$,$Rs. 28$,and $Rs. 32$ respectively,then the ratio of their shares becomes $9: 13: 8$. What is the amount (in $Rs.$) given to $A$?

In two alloys,gold and silver are in the ratios of $4:1$ and $1:3$. After alloying together $10 \text{ kg}$ of the first alloy,$16 \text{ kg}$ of the second,and several kilograms of pure gold,an alloy was obtained in which the ratio of gold to silver was $3:2$. Find the weight of the new alloy (in $\text{kg}$).