R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: TEST YOURSELF

The sum of the squares of two consecutive positive odd numbers is $514$. Find the numbers.

The sum of the squares of two consecutive positive even numbers is $452$. Find the numbers.

Find two consecutive positive odd integers whose product is $483$.

The sum of a natural number and its reciprocal is $\frac{65}{8}$. Find the number.

Divide$57$ into two parts whose product is $680$.

Also find the value when the smaller part is subtracted by the larger part?

A man is $3\frac{1}{2}$ times as old as his son. If the sum of the squares of their ages is $1325$, find the ages of the father and the son.

A train covers a distance of $300 \mathrm{km}$ at a uniform speed. If the speed of the train is increased by $5\mathrm{km}/\mathrm{hour}$, it takes$2$ hours less in the journey. Find the original speed of the train.

The speed of a boat in still water is $15 \mathrm{km}/\mathrm{hr}.$ It goes $30 \mathrm{km}$ upstream and returns back at the same point in $4$ hours $30$ minutes. Find the speed of the stream.