Question

If the denominator of a fraction is multiplied by 2 and the numerator is increased by 2, the fraction becomes $\frac{1}{2}$. If instead, the numerator is multiplied by 2 and the denominator is increased by 2, it becomes $\frac{6}{7}$ What is the sum of the numerator and the denominator of the original fraction (in the lowest form) ? 

• A. 11
• B. 7
• C. 6
• D. 8

Answer 1

Answer:

D. 8

Calculation:

Let the fraction is $\frac{x}{y}$

According to the problem statement,

If we multiply the denominator by 2 and increase the numerator by 2, the resulting fraction is $\frac{1}{2}$

. 

$⇒\frac{(x + 2)}{(2y)}=\frac{1}{2}$

⇒ x  = y - 2                     -----(1)

Next, if we multiply the numerator by 2 and increase the denominator by 2, the resulting fraction is $\frac{6}{7}$

. 

$⇒\frac{(2x)}{(y+2)}=\frac{6}{7}$

⇒ 7x = 3y + 6

⇒ 7(y -2) = 3y + 6         [From equation (1)]

⇒ 7y - 3y = 6 + 14

⇒ 4y = 20

⇒ y = 5

From equation (1)  

x = 5 - 2 = 3

Hence,

Required sum = 5 + 3 = 8

∴ The correct answer is 8.