Question

if we add 5 to the denominator and subtract 5 from the numerator of a fraction 1/8. if we subtract 3 from the numerator and add 3 to its denominator it reduce to 2/7 .find the fractiom​

Answer 1

Step-by-step explanation:

let the fraction be

$\frac{x}{y}$

by first condition

$\frac{x - 5}{ y + 5} = \frac{1}{8}$

8(x-5) = y+5

8x-40= y+5

8x-y = 45. ( equation 1)

by second condition

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

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

7x-21= 2y+6

7x- 2y= 27 (equation 2)

now multiply equation 1 by 2

16x-2y=90

now subtract equation 2 from 1

16x-2y=90

7x-2y=27

-. +. -. ( changing signs )

------------------

9x. = 63

x. =63/9

x = 7

put value of x i n equation 1

8x - y = 45

8(7)-y = 45

56 -y. = 45

y. = 56- 45

y. = 11

The fraction is

$\frac{x}{y} = \frac{7}{11}$