Kerala Board Solutions for Chapter: Pairs of Equations, Exercise 1: Exercise 1

In a rectangle of perimeter one metre, one side is five centimetres longer than the other. What are the lengths of the sides?

A class has $4$ more girls than boys. On a day when only $8$ boys were absent, the number of girls was twice that of the boys. How many girls and boys are there in the class?

A man invested $10000$ rupees, split into two schemes, at annual rates of interest $8\%$ and $9\%.$ After one year he got $875$ rupees as interest from both. How much did he invest in each?

A three and a half metre long rod is to be cut into two pieces, one piece is to be bent into a square and the other into an equilateral triangle. The length of their sides must be the same. How should it be cut?

The distance travelled in $t$ seconds by an object starting with a speed of $u$ metres/second and moving along a straight line with speed
increasing at the rate of $a$ metres/second every second is given by $ut+\frac{1}{2}a{t}^2$ metres. An object moving in this manner travels $10$ metres in $2$ seconds and $28$ metres in $4$ seconds. With what speed did it start? At what rate does its speed change?