Question

8. What is the ratio of the -
(a) number of even numbers to odd numbers from set of natural numbers from 30 to 50?
(b) prime numbers and composite numbers from set of natural numbers from 1 to 20?

Answer 1

$<b>$

(a)
• Even Numbers from 30 to 50:
30, 32 , 34, 36, 38 , 40, 42, 44, 46, 48, 50

Number of Even Numbers from 30 to 50 = 11

• Odd Numbers from 30 to 50:
31, 33, 35, 37, 39, 41, 43, 45, 47, 49

No. of Odd Numbers from 30 to 50 = 10

--- The Number of even numbers to odd numbers from set of natural numbers from 30 to 50 = $\frac{11}{10}$

Required Ratio = 11:10

(b)
• Prime Numbers from 1 to 20:
2, 3, 5, 7, 11, 13, 17, 19

No. of Prime Numbers from 1 to 20 = 8

• Composite Numbers from 1 to 20:
1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18

No. of Composite Numbers from 1 to 20 = 11

--- The Number of Prime numbers and composite numbers from set of natural numbers from 1 to 20 = $\frac{8}{11}$

Required Ratio = 8:11

Answer 2

Gívєn :

• (a) number of even numbers to odd numbers from set of natural numbers from 30 to 50?
• (b) prime numbers and composite numbers from set of natural numbers from 1 to 20?

Tσ fínd :

• The ratio of :–
• Number of even and odd numbers
• Number of prime numbers

Sσlutíσn :

• Odd and even numbers from 30–50.
• To count the numbers fast, use this:

1. 30+50=80
2. 32+48=80
3. 34+46=80

• And so on and the result will be 80x5 PLUS the 40 in the middle which equals 440.

And the odd numbers

1. 31+49=80
2. 33+47=80

And so on and the result will be 80x5 which equals 400

Odd : Even = 440:400

:$\implies\sf\frac{\cancel{440}}{\cancel{400}}$

We get 11:10.

$\rule{100}1$

• Prime Numbers from 1 to 20: 2, 3, 5, 7, 11, 13, 17, 19
• No. of Prime Numbers from 1 to 20 = 8
• Composite Numbers from 1 to 20: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18
• No. of Composite Numbers from 1 to 20 = 11

The Number of Prime numbers and composite numbers from set of natural numbers from 1 to 20 =

Required Ratio = 8:11