Question

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.​

Answer 1

Let us assume thenumerator to be =x

Let us assume thedenominator to be =y

Hence the fractionbecomes=x/y

Accordingtothe given condition

(x−1)/y=1/3

⇒y=3x−3 ———-(i)

Accordingtothesecond givencondition,

x/(y+8)=1/4

⇒y+8=4x

⇒y=4x−8 ————(ii)

Combining(i)and(ii) we get,

3x−3=4x−8

⇒3x−4x=−8+3

−x=−5

⇒x=5

from(i)

y=15−3=12

So,the fraction is =5/12

Answer 2

Answer:

Let the fraction be x/y. 

Given that, the fraction becomes 1/3 when 1 is subtracted from the numerator.

(x - 1)/y = 1/3

3(x - 1) = y

3x - 3 = y

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

Given that, the fraction becomes 1/4 when 8 is added to its denominator.

x / (y + 8) = 1/4

4x = y + 8 

4x - y = 8 ------------ (2)

By solving equations (1) & (2) by the method of elimination, we get:

     3x - y = 3

(-) 4x - y = 8

   -x         = -5

Therefore, x = 5

From equation (1): 3x - y = 3

3 × (5) - y = 3

15 - y = 3

-y = 3 - 15

- y = -12

y = 12

Thus, the fraction, x/y = 5/12

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