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Numerator and denominator of fraction has sum is 12. If 3 is added in the denominator, the fraction becomes 12. Find the fraction so obtained.
CBSE | Class 10 | Exercise 3.8 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
Numerator and denominator of fraction has sum is 12. If 3 is added in the denominator, the fraction becomes 12. Find the fraction so obtained.

Let the numerator be A and the denominator be B.

So, the required fraction is A/B.

ATQ,

The sum of the numerator and denominator of the fraction is 12.

A+B=12

⇒ A+B-12=0

ATQ,

If 3 is added in the denominator, the fraction becomes 12

Use this equation which is given in the question, 

A/(B+3)=1/2

⇒ 2A=(B+3)

⇒ 2A-B-3=0

⇒ 2A-B=3

Hence, two equations are,

A+B-12=0…… (a)

2A-B-3=0…….. (b)

Add (a) and (b), we will get

A+B-12+(2A-B-3)=0

⇒ 3A-15=0

⇒ 3A=15

⇒ A=5

Use the obtained value of A=5 in (a), and find B

5+B-12=0

5+B=12

⇒ B=7

Therefore, the fraction is 5/7.

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