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

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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

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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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APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 9th Mathematics Answers Guide
Chapter 3 Algebra
Exercise 3.14 | Q 2 | Page 133
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