Question

if 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 3/4. If 1 is added to its numerator and to its denominator, the resulting value is 4/5. Find the fraction.

Answer 1

let the fraction = x/y

Now ,

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

4x-4= 3y-3

4x-3y=1 ........ equation 1

&

(x+1)/(y+1)= 4/5

5x+5=4y+4

5x-4y= -1 ....... equation 2

after solving equation 1 & equation 2 :

we get ,

x=7 and y=9.

so , the fraction is = 7/9 .

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Answer 2

Answer:

The answer is 7/9.

Step-by-step explanation:

Let the numerator and denominator be x and y respectively.

According to question,

x- 1 /y- 1 = 3/4

4x-4 = 3y-3

4x = 3y+1

x = 3y+1/4 -----(1)

and, x+1/y+1 = 4/5

5x+5 = 4y+4

5x = 4y-1

x = 4y-1/5 -----(2)

From (1) and (2),

3y+1/4 = 4y-1/5

15y+5 = 16y-4

15y-16y = -4-5

-y = -9

y = 9

Putting the value of y in equation (1),

x = 3(9)+1/4

x = 27+1/4

x = 28/4

x = 7

So the fraction is 7/9.