Question

when 9 is added to the numerator and 1010 is subtracted from the denominator of a fraction the fraction becomes 4 by 3 when 5 is added to the denominator of the fraction and one is extracted from its numerator the fraction = 1 by 3 find the fraction

Answer 1

Hi ,

let the numerator = x

denominator = y

1) if 9 is added to the numerator and 10 is

subtracted from the denominator of a fraction

the fraction becomes 4 / 3

( x + 9 ) / ( y - 10 ) = 4 / 3

3( x + 9 ) = 4 ( y - 10 )

3x + 27 = 4y - 40

3x = 4y - 40 - 27

3x = 4y - 67 ------( 1 )

2 ) when 5 is added to the denominator and

one subtracted from the numerator then the

fraction becomes 1/3

( x - 1 ) / ( y + 5 ) = 1/3

3( x - 1 ) = y + 5

3x - 3 = y + 5

3x - 3 - 5 = y

3x -8 = y

y = 3x - 8 -------( 2 )

put y value in equation ( 1 ) we get ,

3x = 4(3x - 8 ) - 67

3x = 12x - 32 - 67

3x -12x = -99

-9x = -99

x = (- 99 )/ ( - 9 )

x = 11

put x = 11 in equation ( 2 ) we get ,

y = 3 × 11 - 8

y = 33 - 8

y = 25

Therefore ,

required fraction = x / y = 11 / 25

I hope this helps you.

:)