Question

the denominator of a fraction is 2 more than its numerator.when both the numerator and the denominator are increased by 3,the fraction is increased by 3/20.Find the original fraction given that both the numerator and denominator are positive integers

Answer 1

Answer: 3/5

Explanation:

`(a)/(a+2)+(3)/(20)=(a+3)/((a+2)+3)\\\\\\(a)/(a+2)\bigg((20)/(20)\bigg)+(3)/(20)\bigg((a+2)/(a+2)\bigg)=(a+3)/(a+5)\\\\\\(23a+6)/(20(a+2))=(a+3)/(a+5)\\\\\\(23a+6)(a+5)=20(a+2)(a+3)\\\\\\23a^2+121a+30=20a^2+100a+120\\\\\\3a^2+21a-90=0\\\\\\a^2+7a-30=0\\\\\\(a+10)(a-3)=0\\\\\\a=-10\quad a=3`

Since "a" is a positive integer, disregard a = -10

So the only valid answer is a=3 → a+2=5

`(a)/(a+2)=\large\boxed{(3)/(5)}`