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 the fraction be x/y
A. To. Q
(x-1)/y=1/3
3x-3=y
3x-y=3------------------------eq(1)
x/(y+8)=1/4
4x=y+8
4x-y=8--------------------------eq(2)
eq(1)-eq(2)
-x=-5
x=5
Put x=5 in eq(1)
15-y=3
y=12
Hence the fraction is5/12

Answer 2

Given :

• A fraction becomes 1/ 3 when 1 is subtracted from the numerator.

• It becomes 1/ 4 when 8 is added to its denominator.

To Find :

The required fraction.

Solution :

Let the fraction be $\sf\dfrac{x}{y}$

According to the given information :

$\\ \sf \: \: \frac{x - 1}{y} = \frac{1}{3} \\ \\ \\ \implies \sf \: 3x - y = 3 \: \qquad \: (i) \\ \\ \\ \sf \: \frac{x}{y + 8} = \frac{1}{4} \\ \\ \\ \implies \sf \: 4x - y = 8 \: \qquad \: (ii) \:$

Subtracting equation 1 from equation 2, we obtain :

x=5

Putting this value in equation 1 :

$\\ \sf \: 3x - y = 3 \\ \\ \\ \implies \sf \: 3(5) - y = 3 \\ \\ \\ \implies \sf \: 15 - y = 3 \\ \\ \\ \implies \sf \: y = 12$

Hence, the fraction is $\sf\dfrac{5}{12}$