Question

A GENIUS can only solve this question.

The sum of the numerator and the denominator of a fraction is 9. If one is added to the numerator and one is subtracted from the denominator, it reduces to 1/2. Find the fraction.​

Answer 1

Answer:

2/7

Step-by-step explanation:

Let the numerator be x and the denominator be y.

So the fraction will be x/y.

sum of the numerator and the denominator of a fraction is 9.

x + y = 9

=> x = 9 - y    ----- (1)

One is added to the numerator and one is subtracted from the denominator, it reduces to 1/2.

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

=> 2(x + 1) = y - 1

=> 2x + 2 = y - 1

=> 2(9 - y) + 2 = y - 1

=> 18 - 2y + 2 = y - 1

=> 20 - 2y = y - 1

=> 20 + 1 = y + 2y

=> 21 = 3y

=> y = 7

Place y = 7 in (1), we get

x = 9 - y

=> x = 9 - 7

=> x = 2

Therefore,

Fraction = 2/7.

Hope it helps!