Jose Paul Solutions for Chapter: Simple Equations, Exercise 4: EXERCISE 8.3

The length of a rectangle exceeds its width by $4 \mathrm{m}$. If its perimeter is $40 \mathrm{m}$, find its dimensions.

Here is a square. Find the value of $x$ and also the length of the side of the square.

The length of a rectangle exceeds its width by $5 \mathrm{m}$. The width is increased by $1 \mathrm{m}$ and the length is decreased by $2 \mathrm{m}$. The area of new rectangle is $4 \mathrm{sq} \mathrm{m}$ less than the area of the original rectangle. Find the dimensions of the original rectangle.

The length of a rectangle exceeds its width by $3 \mathrm{m}$. If the width is increased by $4 \mathrm{m}$ and length is decreased by $6 \mathrm{m}$, the area is decreased by $22 \mathrm{sq}. \mathrm{m}$. Find the dimensions of the rectangle.

Two ships leave their base at $725 \mathrm{km}$ apart. They travel towards each other at rates equal to $30$ and $35 \mathrm{km}/\mathrm{hr}$. If in $x$ hours will they be $75 \mathrm{km}$ apart, then find the value of $x$.

A car leaves Agra at $11 \mathrm{a}.\mathrm{m}.$ travelling at $50 \mathrm{km}/\mathrm{hr}$. If a second car travelling at $x \mathrm{km}/\mathrm{hr}$ leaves Agra an hour later and overtakes the first car at $5 \mathrm{pm}$, then find the value of $x$.

The sum of the digits of a two-digit number is $7$. If the digits are reversed, the number formed is $9$ less than the original number. Find the number.

The sum of the digits of a two-digit number is $10$. If we reverse the digits, the new number will be $54$ more than the original number. What is the original number?