## the denominator of a fraction is greater than its numerator by 9.if 7 is subtracted from both,its numerator and denominator, the fraction be

Question

the denominator of a fraction is greater than its numerator by 9.if 7 is subtracted from both,its numerator and denominator, the fraction becomes 2/3.find the original fraction.

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4 months 2021-09-24T21:07:30+00:00 2 Answers 0 views 0

25/34

Step-by-step explanation:

let the numerator be x

so the denominator is x+9

ATQ

⇒x-7/x+9-7=2/3

⇒x-7/x+2=2/3

⇒3(x-7)=2(x+2)

⇒3x-21=2x+4

⇒3x-2x=4+21

∴x=25

so the numerator is 25 and denominator is 25+9=34

so the number is 25/34

Step-by-step explanation:

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,

denominator = 18.

So original fraction is 11/18.

3/11th of original fraction is

= 11/18 x 3/11

= (11×3)/(18×11)

= 3/18

=1/6