When the numerator of a fraction is increased by 6 and the denominator by 15, the overall fraction is increased by 20%. If on decreasing the denominator by 6, the fraction is increased by 150%, find the fraction.

When the numerator of a fraction is increased by 6 and the denominator by 15, the overall fraction is increased by 20%. If on decreasing the denominator by 6, the fraction is increased by 150%, find the fraction. Correct Answer 3/10

Let the numerator and denominator of the fraction be ‘x’ and ‘y’ respectively

When numerator is increased by 6 and denominator by 15,

⇒ (x + 6)/(y + 15) = 120% of x/y

⇒ (x + 6)/(y + 15) = 6x/5y

⇒ 5xy + 30y = 6xy + 90x

⇒ 90x + xy = 30y      ----(1)

When the denominator is decreased by 6,

⇒ x/(y – 6) = 250% of x/y

⇒ x/(y – 6) = 5x/2y

⇒ 2y = 5y – 30

⇒ y = 30/3 = 10

Substituting in (1),

⇒ 90x + 10x = 300

⇒ x = 300/100 = 3