Q8. The sum of the square of three consecutive natural numbers is 302. What is the middle number?

A. 10

B. 12

C. 8

D. 15

Answer- Option A

Explanation-

Let the smallest number be x. Then other two numbers be (x + 1) and (x + 2) x + (x + 1) + (x + 2) = 302 x = 9 Hence, the middle number is 10

Q9. The sum of two number is 42, and their product is 440. Find the sum of their reciprocals?

A.

21

220

B.

8

75

C.

75

4

D.

220

21

Answer- Option A

Explanation-

Let two numbers be x and y We are given in the question, (x + y) = 42, xy = 440

1

x

+

1

y

=

x + y

xy

=

42

440

=

21

220

Q10. The difference between two natural number is 3. And the sum of their squares is 549, what is the sum of the numbers?

A. 81

B. 27

C. 33

D. 25

Answer- Option C

Explanation-

Let the numbers be x and (x + 3) Then, x^{2} + (x + 3)^{2} = 549 x^{2} + 3x - 270 = 0 x = 15 and x = 18 The numbers are 15 and 18 Hence, the sum of these numbers is 15 + 18 = 33

Q11. If 16 is added to a positive number is becomes equal to 80 times the reciprocal of the number. The positive number is?

A. 4

B. 10

C. 12

D. 3

Answer- Option A

Explanation-

Let the number be x. Then

x + 16

=

80

x

x^{2} + 16x - 80 = 0 (x + 20)(x - 4) = 0 x = 4

Q12. The ratio between two numbers is 4 : 7. If each is increased by 4, the ratio becomes 3 : 5. Find the larger number?

A. 36

B. 48

C. 64

D. 56

Answer- Option D

Explanation-

Let the two numbers be 4x and 7x According to the question,

4x + 4

7x + 4

=

3

5

20x + 20 = 21x + 12 x = 8 The larger number is 7*8 = 56

Q13. The sum of three number is 95. If the first number is thrice the second number and the third number is one-fourth of the first number then the second number is?

A. 50

B. 20

C. 35

D. 40

Answer- Option B

Explanation-

Let second number be x Then, first number is 3x and third number is

1

4

(3x)

3x

+

x

+

3x

4

=

95

19x

4

=

95

x = 20 So, the second number is 20

Q14. The sum of two numbers is 15. Twenty times one number is equal to ten times the second number. Find the bigger number?

A. 8

B. 7

C. 5

D. 10

Answer- Option D

Explanation-

Let the numbers be x and (15 - x) 20x = 10(15 - x) x = 5 So, the two numbers are 5 and 10 The bigger number is 10