Question

If 5 is added to both the numerator and denominator of a fraction it becomes 2/3 but when 1 is subtracted from both numerator and denominator it becomes 1/3. find the fraction.​

Answer 1

The fraction is $\frac{3}{7}$ .

• Let the numerator of the fraction be x and denominator be y.
• The denominator and numerator is added by 5 then the fraction becomes 2/3.

$\frac{x+5}{y+5}  =\frac{2}{3}$

3x + 15= 2y + 10

3x - 2y = -5         ........(Equation 1)

• Now when the denominator and numerator is subtracted by 1 then the fraction becomes 1/3.

$\frac{x-1}{y-1} = \frac{1}{3}$

3x - 3 = y - 1

3x - y = 2    .........(Equation 2)

• Subtracting equation 2 from equation 1

-y = -7

y = 7

• Substituting the value of y in equation 1 we get

3x - 14 = -5

3x = 9

x = 3

• The required fraction with numerator(x) = 3 and denominator(y) = 7.
• The fraction becomes $\frac{3}{7}$ .