Question

if 1 is added to the numerator of a fraction it becomes 1/5;if 1 is taken from the denominator it becomes 1/7. find the fraction


please answer fast

Answer 1

Let the numerator be x and denominator be y.

Then the resultant fraction will be x/y.  --------- (*)

Given that if 1 is added to the numerator of a fraction, it becomes 1/5.

x + 1/y = 1/5

5x + 5 = y

5x - y = -5 ------ (1)


Given that if 1 is taken to the denominator, it becomes 1/7.

x/y - 1 = 1/7

7x = y - 1

7x - y= -1   ----- (2)


On solving (1) and (2), we get

5x - y = -5

7x - y = -1
--------------------

-2x = -4

x = 2.


Substitute x = 2 in (1), we get


5x - y = -5

5(2) - y = -5

10 - y = -5

y = 15.


Substitute x and y in (*), we get

The fraction = 2/15.


Verification:

x + 1/y = 1/5

2 + 1/15 = 1/5

3/15 = 1/5

1/5 = 1/5.


x/y - 1 = 1/7

2/15 - 1 = 1/7

2/14 = 1/7

1/7 = 1/7.


Hope this helps!