Question

If 4 is added to the numerator of the fraction and 5 is subtracted from its denominator,the fraction becomes 3.If 1 is subtracted from the numerator and 2 is added to the denominator,the fraction becomes 2/5.Find the fraction ​

Answer 1

Answer:

5/8 is the Fraction in the simplest form.

Step-by-step explanation:

So let's assume the fraction as x / y.

Now, (x + 4) / (y - 5) = 3

⇒ x + 4 = 3y - 15  

      Multiply the equation with 5;

⇒ 5x +20 = 15y - 75

⇒ 5x = 15y - 95                

Also given that, (x - 1) / (y + 2) = 2/5

⇒ 5x - 5 = 2y + 4

We know 5x = 15y - 95

⇒ 15y - 95 - 5 = 2y + 4

⇒ 13y = 104

⇒ y = 104/ 13

∴ y = 8

Now put it in any equation like :

(x - 1) / (y + 2) = 2/5

⇒ (x - 1) / (8 + 2) = 2/5

⇒ x - 1 = 4

∴ x = 5

Hence the simplest form of the fraction is 5/8.