Question

14. In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2\3. Find the original number.


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Answer 1

Answer:

let the numerator be x

denominator = 2x-2

3 is added :-

Numerator= x+3

Denominator= 2x-2+3

=2x+1

x+3/2x+1=2/3

3(x+3)=2(2x+1)

3x+9=4x+2

3x-4x=2-9

-x=-7

x=7

Original Numerator = x = 7

Original Denominator = 2x-2

= 2(7)-2

= 14-2

= 12

Original Fraction = 7/12

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Answer 2

Answer:Let the numerator be x

Denominator = 2x − 2

Therefore the fraction = x/2x − 2

Given when 3 is added to both the numerator and denominator, the fraction becomes 2/3.

Hence (x + 3)/(2x  − 2 + 3) = 2/3  

⇒ (x + 3)/(2x + 1) = 2/3  

⇒ 3x + 9 = 4x + 2  

⇒ x = 7

Therefore the fraction is 7/12.

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