Question

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$. Find the fraction.​

• A. $\frac{3}{5}$
• B. $\frac{2}{3}$
• C. $\frac{5}{7}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{5}{7}$

Assume, required fraction is $\frac{x}{y}$

The sum of the numerator and denominator of the fraction is 12. So,​

x + y = 12​

⇒ x + y – 12 = 0​

If the denominator is increased by 3, the fraction becomes $\frac{1}{2}$.​

$\frac{x}{(y+3)}=\frac{1}{2}$​

⇒ 2x = (y + 3)​

⇒ 2x – y – 3 = 0​

The two equations are,​

x + y – 12 = 0…… (i)​

2x – y – 3 = 0…….. (ii)​

Adding (i) and (ii), we get​

x + y – 12 + (2x – y – 3) = 0​

⇒ 3x - 15 = 0​

⇒ x = 5​

Using x = 5 in (i), we find y​

5 + y – 12 = 0​

⇒ y = 7​

Therefore, the required fraction is $\frac{5}{7}.$

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