Question

If the numerator and denominator of a fraction are each decreased by 3, the fraction becomes 2/3. If both the numerator and the denominator are increased by 7, the fraction becomes ¾. Find the fraction?

Answer 1

let numerator be x
denominator be y
IN CASE 1
x-3/y-3=2/3
3(x-3)=2(y-3)
3x-9=2y-6
3x-2y=-6+9
3x-2y=3. 1
IN CASE 2
x+7/y+7=3/4
4(x+7)=3(y+7)
4x+28=3y+21
4x-3y=-7. 2
from 1 and 2
by elimination method
4(3x-2y=3)
3(4x-3y=-7)
therefore 12x-8y=12
12x-9y=-21
by the sign changing of 12x-9y=-21
is y=33
by putting the value of y in 1or2 equation
3x-2(33)=3
is = 23