## 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 