Question

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?

Answer 1

Answer:

Step-by-step explanation:

Let numerator = x and let denominator = y

According to given condition, we have

$\frac{x+1}{y-1} =1$ $and$ $\frac{x}{y+1} = \frac{1}{2}$

⇒ x + 1 = y – 1 and 2x = y + 1

⇒ x – y = −2 … (1) and 2x – y = 1… (2)

So, we have equations (1) and (2), multiplying equation (1) by 2 we get (3)

2x − 2y = −4… (3)

2x – y = 1… (2)

Subtracting equation (2) from (3), we get

−y = −5⇒ y = 5

Putting value of y in (1), we get

x – 5 = −2⇒ x = −2 + 5 = 3

Therefore, fraction = $\frac{x}{y} = \frac{3}{5}$