The sum of a numerator and denominator of a fraction is 18. If the den

1.	The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.
Answer» Let the numerator be ‘a’ and denominator be ‘b’ Given, Sum of a numerator and denominator of a fraction is 18. ⇒ a + b = 18 ----- (1) Also, If the denominator is increased by 2, the fraction reduces to 1/3. ⇒ a/(b + 2) = 1/3 ⇒ 3a - b = 2 ------ (2) Adding (1) and (2) ⇒ 4a = 20 ⇒ a = 5 Thus, b = 13 Fraction is 5/13

The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.

Answer»

Let the numerator be ‘a’ and denominator be ‘b’

Given,

Sum of a numerator and denominator of a fraction is 18.

⇒ a + b = 18 ----- (1)

Also,

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

⇒ a/(b + 2) = 1/3

⇒ 3a - b = 2 ------ (2)

Adding (1) and (2)

⇒ 4a = 20

⇒ a = 5

Thus, b = 13

Fraction is 5/13