Question

The sum of the numerator and the denominator of a fraction is 67 . When 31 is added to the denominator, the fraction becomes 3/11 . What was the original fraction ?​

Answer 1

Answer:

The original fraction is 21/46

Step-by-step explanation:

Given :

• The sum of the numerator and the denominator of a fraction is 67
• When 31 is added to the denominator, the fraction becomes 3/11 .

To find :

the original fraction

Solution :

Let the numerator of the fraction be x and denominator be y.

Then, the original fraction = x/y

• Numerator + denominator = 67

 x + y = 67

 x = 67 - y

 

• When 31 is added to denominator, the denominator becomes (y + 31)

new fraction = 3/11

 $\longrightarrow \sf \dfrac{x}{y+31}=\dfrac{3}{11}$

Put x = 67 - y,

 $\sf \dfrac{67-y}{y+31}=\dfrac{3}{11} \\\\ \sf 11(67-y)=3(y+31) \\\\ \sf 737-11y=3y+93 \\\\ \sf 11y+3y = 737-93 \\\\ \sf 14y=644 \\\\ \sf y=\dfrac{644}{14} \\\\ \underline{\sf y=46}$

Therefore, the denominator is 46.

Numerator = 67 - y = 67 - 46 = 21

So, the original fraction is 21/46