Chapter 7 - Problems Based On Quadratic Equations Exercise Ex. 7.1

Question 1
The sum of the square of the 2 consecutive natural numbers is 481. Find the numbers.
Solution 1
Question 2
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
Solution 2
Question 3
The sum of the square of 2 consecutive odd positive integers is 290.Find them.
Solution 3
Question 4
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Solution 4
Question 5
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Solution 5
Question 6
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
Solution 6
Question 7
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
Solution 7
Question 8
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
Solution 8
Question 9
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solution 9
Question 10
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
Solution 10
Question 11
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.
Solution 11
Question 12
Solution 12
Question 13
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solution 13
Question 14
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Solution 14
Question 15
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
Solution 15
Question 16
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solution 16
Question 17
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
Solution 17
Question 18
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Solution 18
Question 19
Solution 19
Question 20
Solution 20
Question 21
Solution 21
Question 22
Solution 22
Question 23
Solution 23
Question 24
Solution 24
Question 25
Solution 25
Question 26
Solution 26
Question 27
Solution 27
Question 28
Solution 28
Question 29
Solution 29
Question 30
Solution 30
Question 31
Solution 31
Question 32
Solution 32
Question 33
Solution 33
Question 34
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
Solution 34
Question 35
Solution 35
Question 36
Solution 36
Question 37
Solution 37
Question 38
Solution 38
Question 39
Solution 39
Question 40
Solution 40
Question 41
Solution 41
Question 42
Solution 42
Question 43
Solution 43
Question 44
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Solution 44
Question 45
Divide 25 into two parts such that twice the square of the larger part exceeds thrice the square of the smaller part by 29.
Solution 45
Question 46
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Solution 46
Question 47
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
Solution 47
Question 48
A two digit number is four times the sum and 3 times the product of its digits, find the number.
Solution 48