Question

if one is added to the numerator of fraction, it becomes 1/5; if one is taken from the denominator, it becomes 1/7, find the fraction​

Answer 1

Step-by-step explanation:

let the numerator be x and denominator be y

according to the first condition

(x + 1) / y = 1/5

5x + 5 = y

5x - y = -5 –––––1

according to he second condition

x/ (y - 1 ) = 1/7

7x = y - 1

7x - y = -1 –––––2

subtracting equation 2 from 1

7x -y = -1

5x - y = -5

2x = -6

x = -3

substituting x = -3 in equation 1

5x - y = -5

5(-3) - = -5

-15 - y = -5

-y = -5 + 15

-y = 10

y = -10

Answer 2

Answer:

2/15

Step-by-step explanation:

Let the fraction be x/y

Then according to the given conditions, we have

(x + 1)/y = 1/5

5 (x + 1) = y

5x + 5 = y

⇒ 5x – y = -5 … (i)

And,

x/(y – 1) = 1/7

7x = y – 1

7x – y = -1 … (ii)

Now, subtracting (i) from (ii) we get

7x – y = -1

5x – y = -5

(-)–(+)-(+)—

2x = 4

x = 2

On substituting the value of x in (i), we get

5(2) – y = -5

10 – y = -5

y = 10 + 5

y = 15

Therefore, the fraction is 2/15.