Question

The numerator of a fraction is 5 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

Hii friend,

Let the denominator be X.

Then denominator of the fraction = X-5

Therefore,

Fraction = Numerator/Denominator = X-5/X.

According to question,

X-5+2 / X+9 = 2/3

X-3/X+9 = 2/3

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

3X-9 = 2X+18

3X-2X = 18+9

X = 27

Denominator = X= 27

Numerator = X-5 = 27-5 = 22

Therefore,

Fraction = Numerator/Denominator = X-5/X = 22/27

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

Answer 2

let,
 the denominator be x
Numerator be (x-5)

Fration :- 

$\frac{x-5}{x}$
________________________

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

According to the given information,

$\frac{x-5 + 2}{x + 9} = \frac{2}{3}$

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


Cross mulitply,

3(x-3) = 2(x + 9) 

3x - 9 = 2x + 18 

3x - 2x = 18 + 9

x = 27

____________________

Now,

Fraction is

$\frac{x-5}{x } = \frac{27-5}{27}$

= $\frac{22}{27}$



i hope this will help you



-by ABHAY