## FRANK Solutions for Class 10 Maths Chapter 7 - Problems Based On Quadratic Equations

## 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 60cm

^{2}, find the hypotenuse.
Solution 17

Question 18

The area of right-angled triangle is 600cm

^{2}. 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

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