Question

if 1 is added to both the numerator and denominator of fraction it becomes equal to 7 by 8 if 1 is subtracted from both the numerator and denominator of the same fraction it becomes equal to 6by7 find the fraction

Answer 1

let be the numerator=x and denominator=y
so, the fraction becomes x/y
according to the question,
(x+1)/(y+1)=7/8
(x+1)8=7(y+1)
8X+8=7y+7
8x-7y=8-7
8x-7y=1---------(1)
(x-1)/(y-1)=6/7
(x-1)7=6(y-1)
7x-7=6y-6
7x-6y=7-6
7x-6y=1---------(2)
by substituting in equation 2,
x=(1-6y)/7
put value of x in equation 1,
8[(1-6y)/7]-7y=1
(8-48y)/7-7y=1
8-48y-49y=1×7
8-97y=7
8-7=97y
1/97=y
put value of y in value of x,
x=[(1-6/97)/7]
=(97-6)/7
=91/7
x=13
so,the fraction=13×97/1
=1261/1