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If 2 is added to both numerator and the denominator then the fraction becomes 9/11. If 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
CBSE | Class 10 | Exercise 3.8 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
If 2 is added to both numerator and the denominator then the fraction becomes 9/11. If 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.

Let’s assume the numerator of the fraction to be A and the denominator of the fraction to be B.

So, the required fraction is A/B.

ATQ , 

the equation so formed is,

A+2B+2=9/11

⇒ 11\left( A+2 \right)=9\left( B+2 \right)

⇒ 11A+22=9B+18

⇒ 11A-9B=18-22

⇒ 11A-9B+4=0 ……. (i)

So ATQ, 

We have, 

A+3B+3=56

⇒ 6\left( A+3 \right)=5\left( B+3 \right)

⇒6A+18=5B+15

⇒ 6A-5B=15-18

⇒ 6A-5B+3=0…….. (ii)

Solving (i) and (ii), to find the fraction

By using cross-multiplication method, we have

A-9\times 3-5\times 4=-B11\times 3-6\times 4=111\times -5-6\times -9

A-27+20=-B33-24=1-55+54

A-7=-B9=1-1

A7=B9=1

 A=7,B=9

Hence, the required fraction is 7/9.

i

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