Question

find the fraction which is equal to 1/2 when both the its numerator and denominator are increased by 2. It is equal to3/4 when both are increased by 12

Answer 1

let numerator be x and denominator be y
where x<y
when they are increased by 2
x+2/y+2=1/2
2(x+2)=1(y+2)
2x+4=y+2
2x-y=2-4
2x-y=-2...... (1)
when they are increased by 12
x+12/y+12=3/4
4(x+12)=3(y+12)
4x+48=3y+36
4x-3y=36-48
4x-3y=-12......(2)
multiply eq.(1) BY 3
6x-3y=-6..........(3)
from eq(2) and (3) by elimination method
4x - 3y = -12
6x - 3y = -6
(-)   (-)    (-)
-----------------
-2x    = -6
so, x  = 3
putting the value of 'x' in eq (1)
2(3) - y = -2
6 - y = -2
6 + 2 = y
8 = y
so fraction is 3/8    answer
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