Problems on Numbers with Explanation

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

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?

Answer- Option C

Explanation-

Let the numbers be x and (x + 3)
Then, x² + (x + 3)² = 549
x² + 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?

Answer- Option A

Explanation-

Let the number be x. Then

x + 16

=

80 x

x² + 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?

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?

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?

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