The sum of the numerator and denominator of a fraction is 12. If the d

1.	The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
Answer» Let the numerator be ‘a’ and denominator be ‘b’. Given, Sum of the numerator and denominator of a fraction is 12 . If the denominator is increased by 3, the fraction becomes 1/2. ⇒ a + b = 12 ------ (1) Also, a/(b + 3) = 1/2 ⇒ 2a – b = 3 ------- (2) Adding eq1 and eq2 ⇒ a + b + 2a – b = 15 ⇒ 3a = 15 ⇒ a = 5 Thus, b = 7 Fraction is 5/7.

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.

Answer»

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

Given,

Sum of the numerator and denominator of a fraction is 12 .

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

⇒ a + b = 12 ------ (1)

Also,

a/(b + 3) = 1/2

⇒ 2a – b = 3 ------- (2)

Adding eq1 and eq2

⇒ a + b + 2a – b = 15

⇒ 3a = 15

⇒ a = 5

Thus,

b = 7

Fraction is 5/7.