Question

if the numerator of a fraction is decreased by 1 its value becomes 2/3.But if the denominator is increased by 5vits value becomes 1/2.what is the fraction​

Answer 1

$\huge{\bold{\underline{Solution:}}}$

Let the numerator and denominator be x and y respectively.

A.T.Q,

• Case I

Numerator is decreased by 1 and the denominator remains the same.

This can be represented in the form of linear equation as:

$\Rightarrow \frac{x-1}{y} = \frac{2}{3} \\ \Rightarrow 3x - 3 = 2y \\ \Rightarrow 3x - 2y = 3 \qquad \bold{(1)}$

• Case II

Denominator is increased by 5 but the numerator remains the same.

This can be represented in the form of linear equation as:

$\Rightarrow \frac{x}{y+5} = \frac{1}{2} \\ \Rightarrow 2x = y + 5 \\ \Rightarrow 2x - y = 5 \qquad \bold{(2)}$

Multiply (2) by 2 to make the coefficient of y same.

On Solving (1) and (2), We get

x = 7

Putting x = 7 in (1):

$\Rightarrow 3x - 2y = 3 \\ \Rightarrow 3 \cdot 7 - 2y = 3 \\ \Rightarrow 2y = 21-3 \\ \Rightarrow y = \frac{18}{2} = 9$

Numerator is x and Denominator is y.

Fraction: $\frac{x}{y}$

$\huge{\bold{Answer: \: \frac{7}{9}}}$