Question

If 2 is added to the numerator and denominator it becomes `(9)/(10)` and if 3 is subtracted from the numerator and denominator it becomes `(4)/(5) `Find the fraction.

Answer 1

Let the fraction be `x/y`.

According to given information, we have
`(x + 2)/(y + 2) = (9)/(10)`
and
`(x - 3)/(y - 3) = (4)/(5)`
⇒ 10x + 20
= 9y + 18
and
5x - 15
= 4y - 12
⇒ 10x - 9y = -2  .....(i)
and
5x - 4y = 3          ....(ii)
Multiplying eqn. (ii) by 2, we get
10x - 8y = 6      ....(iii)
Subtracting eqn. (iii) from eqn. (i), we get
-y = -8
⇒ y = 8
⇒ 10x = -(9) = 6
⇒ 10x - 64 = 6
⇒ 10x = 70
⇒ x = 7
∴ Required fraction = `(7)/(8)`.