Question

If 2 is added to the numerator of a fraction,it reduces to1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.​

Answer 1

Answer:

3/10

Step-by-step explanation:

let numerator be n and denominator be d then,

ATQ, n+2/d=1/2

2(n+2)=d

2n+4=d----------eq1st

= n/d-1=1/3

= 3n=d-1

= 3n=2n+4-1(putting the value od d from eq1st)

=3n-2n=4-1

= n=3--------------eq2nd

putting the valur od n in eq1st

2n+4=d

2*3+4=d

6+4=d

10=d

therefore fraction is n/d=3/10

Answer 2

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow \sf \dfrac{x+2}{y}=\dfrac{1}{2}\\\\\longrightarrow 2(x+2) = y \\\\\longrightarrow 2x+4 = y \\\\\longrightarrow 2x-y = -4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(1)$

According to the second condition,

$\longrightarrow \sf \dfrac{x}{y-1}=\dfrac{1}{3}\\\\\longrightarrow 3x = y-1 \\\\\longrightarrow 3x-y = -1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ....................(2)$

Equation (2) - Equation (1),

$\longrightarrow \bf x = 3$

Substitute the value of x in equation (1),

$\longrightarrow \sf 2\times 3 - y = -4 \\\\\longrightarrow 6-y = -4 \\\\\longrightarrow -y = -10\\\\\longrightarrow \bf y = 10$

$\bf FRACTION = \dfrac{3}{10}$