Question

If we add 1 to both the numerator and denominator of a tion and get 2/3, and then subtract two from both numerator and denominator to get 1/3, what is the original tion?

a) 1/2
b) 2/3
c) 3/4
d) 4/5

Answer 1

Solving the system of equations from the given conditions leads to the original fraction being 3/4. Thus, the correct answer is option c)3/4.

Step-by-step explanation:

Let the original fraction be x/y. According to the given information:

1. If we add 1 to both the numerator and denominator, we get (x + 1)/(y + 1) = 2/3.

2. If we subtract two from both the numerator and denominator, we get (x - 2)/(y - 2) = 1/3.

Now, we can set up a system of equations:

Equation 1: (x + 1)/(y + 1) = 2/3

Equation 2: (x - 2)/(y - 2) = 1/3

Cross-multiply to eliminate fractions:

Equation 3: 3(x + 1) = 2(y + 1)

Equation 4: 3(x - 2) = 1(y - 2)

Solve Equations 3 and 4 simultaneously:

By solving, we get x = 3 and y = 4.

So, the original fraction is 3/4, which corresponds to Option C.