Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Linear Equations in one Variable, Exercise 5: Exercise 7.3

The difference between two positive integers is $51$. The quotient when one integer is divided by the other is $4$. Find the two integers.

The numerator of a rational number is less than the denominator by $8$. If the denominator is decreased by $1$ and the numerator is increased by $17$, then the number obtained is $\frac{3}{2}$. Find the rational number.

The denominator of a rational number is greater than its numerator by $3$ . If numerator and denominator are increased by $1$ and $4$, respectively, the number obtained is $\frac{1}{2}$ . Find the rational number.

The ratio of two numbers is $3:5$ . If each number is increased by $10$, the ratio between the numbers so formed is $5:7$. Find the two original numbers.

A $2$-digit number is such that ones digit is $1$ more than the tens digit. The ratio of this number and the number formed by reversing its digits is $5:6$. Find the number.

A rational number is such that its denominator is twice its numerator. If both the numerator and the denominator are increased by $13$, the rational number becomes $\frac{2}{3}$ in the simplest form. Find the rational number.

The length of a rectangle is twice its breadth. If the ratio of the perimeter of the rectangle and its area is $1:2$, find the dimensions of the rectangle.

A fraction is such that the sum of its numerator and denominator is $15$. If $8$ is added to the numerator and $12$ is added to the denominator, the fraction becomes $\frac{3}{4}$. Find the original fraction.