## Linear Equations in two variables

Q1. If the ratio of the length and breadth of a rectangle is 3:2 and the area is 54 square meters, find the length and breadth of the rectangle.

Q2. Find the value of k for which :

2x + 3y – 11 =0

and , 6x – ky + 7 =0

will not have unique solutions.

Q3. The present age of father is three times that of his son. 5 years ago the father was five times the son’s age. Find their present age.

Q4. 20 years ago a father was 4 times as old as his son and 4 years hence he will be twice as old as his son. Find their present age.

Q5. In a two digit number, the digit in the unit’s place is greater than the digit in the tens place by 5. If the number is 3 times the sum of the digits, find the number.

Q6. A bag contains a total number of 60 coins, some are of value 50 paise and others are of 25 paise. If the total amount of money in the bag is Rs 20.50, find the number of coins in each category.

Q7. The sum of three numbers is 98. The ratio of the first to the second is 2:3 and the ratio of the second to the third is 5:8. Find the number’s.

Q8. Divide 54 into two parts such that the double of one part exceeds three times of the other part by 8.

Q9. In 1975, the father’s age was four times that of his son and in 1995, the father’s age was twice that of his son. Find the year in which the son was born.

Q10. The sum of the digits of a two digit number is 11. are the digits are Interchanged the number increases by 45. Find the number.