$A$ person distributes his pens among four friends $A, B, C$ and $D$ in the ratio $\frac{1}{3}: \frac{1}{4}: \frac{1}{5}: \frac{1}{6}$. What is the minimum number of pens that the person should have?

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

If $3P = 2Q$ and $2Q = 3R$,then what is $P:Q:R$?

The ratio between Sumit's and Prakash's age at present is $2:3$. Sumit is $6 \text{ yr}$ younger than Prakash. What will be the ratio of Sumit's age to Prakash's age after $6 \text{ yr}$?

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 $\text{kg}$).

If $40 \%$ of a number is equal to two-thirds of another number,what is the ratio of the first number to the second number?