Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7 when the - Maths - Pair of Linear Equations in Two Variables

Question

Find the fraction which becomes to 2/3 when the numerator is
increased by 2 and equal to 4/7 when the denominator is increased
by 4

Aman Garg · Accepted Answer

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

$\frac{x + 2}{y} = \frac{2}{3} \Rightarrow 3 x + 6 = 2 y \Rightarrow 6 x + 12 = 4 y ... (1) \frac{x}{y + 4} = \frac{4}{7} \Rightarrow 7 x = 4 y + 16 \Rightarrow 7 x - 16 = 4 y ... (2) From (1) and (2), we get 7 x - 16 = 6 x + 12 \Rightarrow x = 28 y = \frac{3 (28) + 6}{2} = \frac{90}{2} = 45$

Thus, the required fraction is $\frac{28}{45}$

Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7 when the denominator is increased by 4.