Question

If the numerator of a fraction is increased by 2 and the denominator by 1, it becomes 5 by 8 and if the numerator and the denominator of the same fraction are each increased by 1,the fraction becomes equal to 1 by 2 . Find the fraction​

Answer 1

$let \: the \: fraction \: be \: \frac{x}{y}$

According to the question ,

$\frac{x + 2}{y + 1} = \frac{5}{8} \\ \\ \implies 8x + 16 = 5y + 5 \\ \\ \implies 8x - 5y + 11 = 0.....(eq.01)$

Also given that ;

$\frac{x + 1}{y + 1} = \frac{1}{2} \\ \\ \implies 2x + 2 = y + 1 \\ \\ \implies 2x - y + 1 = 0...(eq.02)$

We will now solve both the linear equations in two variables by substitution method,

$from \: equation \: 01 \\ \\ 8x = 5y - 11\\ \\ \implies x = \frac{5y - 11}{8} \\ \\ now \: we \: will \: put \: this \: value \: in \: equation \: 2 \\ \\ \\ 2x - y + 1 = 0 \\ \\ \implies 2( \frac{5y - 11}{8}) - y + 1 = 0 \\ \\ \implies \frac{5y - 11}{4} - y + 1 = 0 \\ \\ \implies \frac{5y - 11 - 4y + 4}{4} = 0 \\ \\ \implies \frac{y - 7}{4} = 0 \\ \\ \implies \boxed{y = 7}$

$now \: we \: will \: put \: this \: value \: in \: eq.02 \\ \\ \implies 2x - y + 1 = 0 \\ \\ \implies 2x - 7 + 1 = 0 \\ \\ \implies 2x - 6 = 0 \\ \\ \implies \boxed{x = 3}$

Therefore the fraction is ,

$\frac{3}{7}$

(ANS)

Answer 2

Answer:

Step-by-step explanation: