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.

please help me out...

Answer 1

pls find the attached soln for ur reference

Answer 2

Solution:

Let Numerator and Denominator of fraction be x and y respectively.

•°• Then, Fraction will be x/y.

Now, Following the Question statement!

☞ Case : 1

(x - 1)/y = ⅓

↬ 3(x-1) = y

↬ 3x - 3 = y

↬ 3x - y = 3 ........(i)

☞ Case : 2

x/(y+8) = ¼

↬4x = y + 8

↬ 4x - y = 8 .........(ii)

Here, Solving Equation (i) and (ii) by Elimination method!

3x - y = 3 × 4

4x - y = 8 × 3

•°•

↬ 12x - 4y = 12

↬ 12x - 3y = 24

_________________

- y = - 12

So, Value of y is 12.

Now, Substituting Value of y in Equation (I) , So We get ;

↬ 3x - y = 3

↬ 3x - 12 = 3

↬ 3x = 3 + 12

↬ 3x = 15

↬ x = 15/3

↬ x = 5

So, Value of x is 5.

Hence, Fraction will be 5/12.