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GradeApplication of Linear Equations in Two Variables

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The taxi fare in a city is as follows; For the first kilometre, the fare is Rs. 8 and for the subsequent distance, it is Rs. 5 per km. taking the distance covered as x km and total fare as Rs. y, write a linear equation for this information and draw its graph.

Father 's age is three times the sum of the ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

A father is three times as old as his son. After 12 years, his age will be twice as that of his son then find their present ages?

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the factor.

If 2 is added to the numerator of a fraction, it reduces to $\dfrac{1}{2}$ and if 1 is subtracted from the denominator, it reduces to $\dfrac{1}{3}$. Find the fraction.

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes $\dfrac{1}{4}$. And when 6 is added to the numerator and the denominator is multiplied by 3, it becomes $\dfrac{2}{3}$. Find the fraction.

A two-digit number is such that the product of its digit is 20. If 9 is added to the number, the digits interchange their places. Find the number.

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and Rs. 100 notes only. Meena got 25 notes in all. Find how many notes of Rs. 50 and Rs. 100 she received.

Two ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.

Seven audio cassettes and three video cassettes cost Rs.1110, while five audio cassettes and 4 video cassettes costs Rs.1350. Find the cost of audio cassettes and video cassettes.

Five years ago a man was seven times old as his son. Five years hence, The father will be three times as old as his son. Find their present ages.

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