Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 9th

# The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction - Mathematics

Sum

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

#### Solution

Let the numerator be “x” and the denominator be “y”

∴ The fraction is x/y

By the given first condition

x + y = 12 → (1)

Again by the second condition

x/(y + 3) = 1/2

2x = y + 3

2x – y = 3 → (2)

(1) + (2) ⇒ 3x = 15

x = 15/3 = 5

Substitute the value of x = 5 in (1)

5 + y = 12

y = 12 – 5

= 7

∴ The fraction is 5/7

Concept: Consistency and Inconsistency of Linear Equations in Two Variables
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