Question

In a rational number twice the numerator is two more than the denominator.If three is added to the numerator as well as the denominator,the new fraction is 2/3.Find the original number

Answer 1

Let a be the numerator and b be the denominator.
given:
#  2a = 2+b
b = 2a - 2
# 3+a/3+b=2/3 (substitute b)
3 + a / 3 + 2a -2 = 2/3
3+a/1+2a=2/3 (cross multiply)
9+3a=2+4a
a=7
substitute a in b = 2a -2
b = 12.

Answer 2

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