If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 12 if we only add 1 to the denominator. What is the fraction?

Question :If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 12 if we only add 1 to the denominator. What is the fraction?

The correct answer :Let the fraction be x/y.

According to the problem, if we add 1 to the numerator and subtract 1 from the denominator, we get:

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

Multiplying both sides by y-1, we get:

x+1 = y-1

x = y-2

Now, if we add 1 to the denominator, we get:

x/(y+1) = 12

Substituting x = y-2, we get:

(y-2)/(y+1) = 12

Multiplying both sides by y+1, we get:

y-2 = 12(y+1)

Expanding the right-hand side, we get:

y-2 = 12y + 12

Simplifying, we get:

-11y = -14

y = 14/11

Substituting y = 14/11 into x = y-2, we get:

x = 14/11 – 22/11 = -8/11

However, since the original fraction must be positive (otherwise adding 1 to the numerator and subtracting 1 from the denominator would result in a negative number), we can discard the negative value for x and conclude that the fraction is:

x/y = 8/11

Therefore, the fraction is 8/11.