Question

9. The sum of a numerator and
denominator of a fraction is 18. If the
denominator is increased by 2, the fraction
reduces to V3. Find the fraction *​

Answer 1

Answer:

Let the numerator of fraction be x and denominator of the fraction y.

The fraction is x /y

The sum of the numerator and denominator of a fraction is 18

x + y = 18

x = 18 - y…Eq. 1

If the denominator is increased by 2, then the fraction reduces to 1/3.

Denominator is increased 2 means denominator now is y + 2

x/y + 2 = 1/3

3x = y + 2

y = 3x - 2…Eq..2

Substituting the value of y from Eq..2 to Eq. 1

x = 18 - y

x = 18 - (3x- 2)

x = 18 - 3x + 2

x + 3x = 18 + 2

4x = 20

x = 5

The numerator is 5

Substituting the value of x in Eq..2 to derive value of y

y = 3x - 2

y = 3 × 5 - 2

y = 15 - 2

y = 13

The denominator is 13

The fraction is 5/13

Answer : the fraction is 5/13

Now checking the correctness of answer by adding numerator and denominator

Sum = 5 + 13 = 18

Means answer is correct