Question

When 6 is added to the numerator of a fraction, the numerator becomes twice the denominator. In another fraction, 10 times the denominator exceeds 5 times the numerator by 30. The number of solutions for the given equations is

• A. 0
• B. 1
• C. 2
• D. Infinitely many solutions

Answer 1

The correct option is D

Infinitely many solutions

Case1 : Let the fraction be $\frac{x}{y}$

Given that, $x+6=2y$

$\Rightarrow x-2y+6=0$

Case 2 : Let the fraction be $\frac{x}{y}$

Given that, $10y-5x=30$

$\Rightarrow 5x–10y+30=0.$

From the equations $x-2y+6=0and5x–10y+30=0.$

$\frac{a_1}{a_2}=\frac{1}{5},\frac{b_1}{b_2}=\frac{-2}{-10}=\frac{1}{5},\frac{c_1}{c_2}=\frac{6}{30}=\frac{1}{5}$

$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$\therefore$ The pair of equations has infinite number of solutions.