Question

The sum of numerator and denominator of a fraction is 4 more than twice the numerator if the numerator and denominator are increased by 3 they are in ratio 2:3 determined
the fraction.

Answer 1

3×x/3×y=2/3

x/y=6/9=2/3

so numerator is 2 and denominator is 3

here fraction 4 is twice the numerator so answer is 2/3

Answer 2

Let, the common multiple of the ratio be,'n'

∴ Numerator = (2×n)

                     = 2n

∴ Denominator = (3×n)

                          = 3n

By condition,

3n-3+2n-3 =(2×2n)+4

⇒ 5n-6 = 4n +4

⇒ 5n-4n = 4+6

⇒ n = 10

∴ Numerator = (10×2)-3

                     = 20-3

                      = 17

∴ Denominator= (10×3)-3

                         = 30-3

                         = 27

∴ The fraction is 17/27