Question

A fraction become 4/5 if 1 is added to both numerate and denominator .if however 5 is subtracted from both the numerator and denominator, the fraction become 1/2 find the fraction

Answer 1

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Answer 2

Let the fraction be x/y.
If 1 is added to both the numerator and denominator, it becomes 4/5
Therefore
(x + 1)/(y + 1) = 4/5
5x + 5 = 4y + 4
5x - 4y = - 1 (Eqaution 1)

If 5 is subtracted from both the numerator and the denominator, the fraction becomes 1/2
So, (x - 5)/(y - 5) = 1/2
2x - 10 = y - 5
2x - y = 5 (Equation 2)

Taking equation 1 and 2 as simultaneous equation
2 (5x - 4y = - 1)
5 (2x - y = 5)

10x - 8y = - 2
10x - 5y = 25
Subtracting 10x - 5y = 25 from 10x - 8y = - 2

10x - 8y = - 2
- 10x + 5y = - 25

-3y = - 27
y = - 27/-3
y = 9

2x - 9 = 5
2x = 14
x = 7

The fraction is x/y = 7/9

Hope this helps you.