Find a fraction which reduces to 3/4 when the numerator and denominator are each decreased by 1, and which reduces to 4/5 when the numerator and denominator are each increased by 1.

Answer 1

Let the original fraction be x/y

equation #1 : (x-1)/(y-1) = 3/4
4x - 4 = 3y - 3
4x - 3y = 1

equation #2 : (x+1)/*(y+1) = 4/5
5x + 5 = 4y + 4
5x - 4y = -1

#1 times 4 :16x - 12y = 4
#2 times 3 : 15x - 12y = -3
subtract them ...
x = 7
back in #1
28 - 3y = 1
-3y = -27
y = 9

the fraction was 7/9

check:
6/8 = 3/4 ✔
8/10 = 4/5 ✔