If $78$ is divided into three parts which are in the ratio of $1: \frac{1}{3}: \frac{1}{6},$ the middle part is

An employer reduces the number of his employees in the ratio $9:7$ and increases their wages in the ratio $14:15$. Find the ratio in which the total bill of wages increases or decreases.

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 $Q$?

$A$ sum of ₹ $1,300$ is divided amongst $P, Q, R$ and $S$ such that $\frac{P \text{'s share}}{Q \text{'s share}} = \frac{Q \text{'s share}}{R \text{'s share}} = \frac{R \text{'s share}}{S \text{'s share}} = \frac{2}{3}$. Then $P$'s share is (in ₹):

The ratio between the present ages of Indira and Lizzy is $3:8$,respectively. After $8 \text{ yr}$,Indira's age will be $20 \text{ yr}$. What was Lizzy's age $5 \text{ yr}$ ago (in $\text{yr}$)?

The reciprocals of the square of the numbers $1 \frac{1}{2}$ and $1 \frac{1}{3}$ are in the ratio: