Question

The denominator of a fraction is 7 more than the numerator. If 1 is added to the numerator and 6 is added to the denominator, the value of the fraction will be ½. Find the numerator and the denominator.

Answer 1

Explanation:

let numerator be x and denominerator be y

according to the question equation is

1+x /7+x+6=1/2( do cross multiplication)

7+x+6=2(1+x)

13+x=2+2x

13-2=2x-x

11=x

numerator =x+1=11+1=12

therefore numerator is 12

for denominerator

substitute the value of x in (7+x+6)

=7+11+6

24

Answer 2

Let x=numerator,

y=denominator.

y=x+7 - - - - - (i)

(x+3)/(y+3) = 2/3

(Cross multiply)

3(x+3)=2(y+3)

3x+9=2y+6

(subtract 9 from both sides)

3x+9–9=2y+6–9

3x=2y+6–9

3x=2y-3 - - - - - - - (ii)

(substitute the value of equation (i) into (ii))

3x=2(x+7)-3

3x=2x+14–3

3x=2x+11

(subtract 2x from both sides)

3x-2x=2x+11–2x

x=11.

(substitute the value of x into equation (i))

y=7+11

y=18.

so numerator =11,

numerator =11,denominator = 18.

So original fraction is 11/18.

3/11th of original fraction is

= 11/18 x 3/11

= (11x3)/(18x11)

= 3/18

=1/6.

Answer = 1/6.