Shyam Saraf and Abhilasha Swarup Solutions for Exercise 1: EXERCISE

From each of any two given numbers, half the smaller number is subtracted. Of the resulting numbers, the larger one is twice as large as the smaller one. What is the ratio of the two numbers?

Two numbers are in the ratio $3 : 4$ such that the sum of their cubes is $728$. Find the larger number.

The ratio of the sum of the squares of the first n natural numbers to the sum of the first n natural numbers is $11 : 3$. Find the value of $n$.

The value of a set of gold coins varies as the square of their radius, if the thickness remains constant; and it varies as the thickness if the radius remains constant. If the radii of the two coins are in the ratio $8:5$, what should be the ratio of their thicknesses, if the value of the first is two times that of the second?

If the ratio of the number of animals to the number of humans on earth is $x$, and the ratio of humans to animals is $y$, then $4$ (Humans $+$ Animals) is _____.

The sum of three numbers is $196$. If the ratio of the first to the second is $2:3$, and that of the second to the third is $5:8$, then the third number is _____.

$\mathrm{A}$ and $\mathrm{B}$ invested some amount in a business deal. The profit was divided in the ratio $2:3$. If A invested $\mathrm{Rs}.8,000$, what was $\mathrm{B}$'s investment?

Four friends $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$ share $\mathrm{Rs}.21000$ in ratio of $\frac{1}{3}:\frac{1}{6}:\frac{1}{8}:\frac{1}{4}$. What is the difference between the share of $(\mathrm{P}+\mathrm{Q})$ and $(\mathrm{Q}+\mathrm{S})$.