Question

The numerator of a fraction is 7 less than its denominator if the denominator is increased by 9 and the numerator by 2 the fraction becomes 2 by 3 find the fraction

Answer 1

Hi friend,

Let the Denominator be X

Then numerator =X-7

Fraction = Numerator/ Denominator = X-7/X

According to question,

X-7+2/X+9 = 2/3

X-5/X+9 = 2/3

3(X-5) = 2(X+9)

3X-15 = 2X+18

3X-2X = 18+15

X = 33

Denominator = X = 33

Numerator = X-7 = 33-7 = 26

Therefore,

Fraction = Numerator/Denominator = X-7/X = 26/33

HOPE IT WILL HELP YOU..... :-)

Answer 2

Let,

Denominator be x
Numerator be (x-7) 

Fraction  = $\frac{x-7}{x}$
____________________________

If Denominator increases by 9 and numerator by  2 , fraction becomes,$\frac{2}{3}$

$\frac{x - 7 +2 }{x + 9} = \frac{2}{3}$


Cross multiplication,

3(x - 7 + 2) = 2(x + 9) 

3(x -5) = 2x + 18 

3x - 15 = 2x  + 18 

3x - 2x = 18 + 15

x = 33
______________

Fraction,

$\frac{x-7}{x} = \frac{33 - 7}{33}$

= $\frac{26}{33}$




i hope this will help you


-by ABHAY