Question

Find the numerator and denominator of a fraction which becomes equal to 1/2 if the
numerator is doubled and denominator is increased by 9 and which becomes equal to 1/4 if
the numerator is halved and the denomionator is decreased by 1.(Ans. Nr = 5, Dr = 11)​

Answer 1

Answer:

let fraction is x/y

2x/(y+9) =1/2

4x=y+9

4x-y=9 (1)

halved means half so

x/2(y+1) =1/4

x/(2y+2) =1/4

4x=2y+2

taking 2 common by both sides

2x-y=1 (2)

from (1) equation y=4x+9 put in 2nd equation

2x-(4x+9) =1

2x-4x-9 = 1

-2x =1+9

x= -5 now put value of x in (2) equation

2(-5) -y =1

-10-y=1

-y=11

y= -11

so fraction is -5/-11 =5/11