Question

Find the Fraction which is equal to ½ when both its numerator and denominator are increased by 1 and which is equal to ⅔ when both are increased by 4.​

Answer 1

$\huge{\bf{\orange{\fbox{\underline{\color{blue}{Answer}}}}}}$

☆ Let the numerator be x and denomentar be y

(x+2)/(y+2)=1/2

2x+4=y+2

2x-y=-2

4x-2y=-4

¤ when

(x+12)/(y+12)=3/4

4x+48=3y+36

4x-3y=-12

▪︎ from both the eq

y=2

x=5

so fraction is

$\huge{\bf{\pink{\fbox{\underline{\color{green}{2/5}}}}}}$

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Answer 2

Answer:

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

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$\frac{x + 1}{y + 1} = \frac{1}{2}$

$\frac{x + 4}{y + 4} = \frac{2}{3}$

$2x + 2 = y + 1$

$3x + 12 = 2y + 8$

$2x - y = - 1............(i)$

$3x - 2y = - 4 \: ...........(ii)$

Multiply Equation (i) by 2 ,

$4x - 2y = - 2 \: \: \: \: \: ..........(iii)$

Subtracting Equation (ii) From Equation (iii) ,

We Have,

$x = 2$

Substituting this value of x in Equation (i) ,

We have,

$2 \times 2 - y = - 1$

$y = 4 + 1$

$= 5$

Hence,

The Required Fraction = $\frac{2}{5}$.