The numerator of a certain fraction is to its denominator as 2 to 3; if five be added to the numerator ratio will be as 3 to 2; what is the fraction?

Mathematics · High School · Tue Nov 03 2020

llm

Answered on Mon Apr 04 2022

Let the numerator be x

and, denominator be y

then, according to question

x/y = 2/3 ….1

Now, 5 is added to the numerator which makes the fraction 3/2

so, (x+5)/y = 3/2

2x + 10 = 3y …..2

From equation 1

x = 2y/3

now, putting value of x in equation 2, we get

2(2y/3) + 10 = 3y

4y + 30 = 9y

9y - 4y = 30

5y = 30

y = 30/5

y = 6

Now, putting value of y in equation 1, we get

x/6 = 2/3

x = 6*2/3

x = 4

Thus, the fraction is 4/6