Question

If 2 is added to number of fraction it reduces to 1/2 and if 1 is subtracted from denominator , it reduces to 1/3 . find fraction.​

Answer 1

Let the unknown fraction be :

⟹ x/y

Wherein :

⟹ ‘x’ is the numerator

⟹ ‘y’ is the denominator

It is given that, if 2 is added to the numerator, it reduces to 1/2.

So, we get :

⟹ x + 2/y = 1/2

Cross multiplying them :

⟹ 2 (x + 2) = y

⟹ 2x + 4 = y

⟹ 2x – y = – 4 . . . . . . . 【 eq · 1 】

Also, it is given that, if 1 is subtracted from the denominator, it reduces to 1/3.

Here, we get :

⟹ x/y – 1 = 1/3

Cross multiplying them :

⟹ 3x = y – 1

⟹ 3x – y = – 1 . . . . . . . . 【 eq · 2 】

Now, we’ll find the value of x by subtracting eq · 1 from eq · 2 :

⟹ (3x – y) – (2x – y) = – 1 – (– 4)

⟹ 3x – 2x – y + y = – 1 + 4

⟹ x = 3

Substituting the value of x in eq · 2 to get y :

⟹ 3x – y = – 1

⟹ 3 (3) – y = – 1

⟹ 9 – y = – 1

⟹ – y = – 1 – 9

⟹ – y = – 10

⟹ y = 10

Putting the values of x and y in the fraction form :

⟹ x/y

⟹ 3/10

━━━━━━━━━━━━━━━━━

Therefore, the required fraction is 3/10.

Answer 2

Answer:

• The original fraction is 3 / 10

Step-by-step explanation:

Given:

• If 2 is added to numerator of fraction it reduces to 1/2
•  if 1 is subtracted from denominator , it reduces to 1/3

To Find:

• The original fraction

Assumptions:

• Let the numerator of the fraction be x
• Let the denominator of the fraction be y

Full Solutions:

✰ According to the question,

$\rightarrow \qquad \tt \dfrac{x+ 2}{y} = \dfrac{1}{2}$

$\rightarrow \qquad \tt 2( x + 2 ) = y$

$\rightarrow \qquad \tt 2x + 4 = y$

$\rightarrow \qquad \tt 2x - y = - 4 ---( 1 )$

✰ As per the other statement,

$\rightarrow \qquad \tt \dfrac{x }{y - 1} = \dfrac{1}{3}$

$\rightarrow \qquad \tt 3x = y - 1$

$\rightarrow \qquad \tt 3x - y = - 1 ---( 2 )$

✰ Subtracting Equations,

$\rightarrow \qquad \tt 3x - y - 2x - y = - 1 - 4$

$\rightarrow \qquad \tt 3x - 2x = - 1 + 4$

$\rightarrow \qquad \tt {\purple{\boxed{\frak{x = 3 }}}\blue\bigstar}$

✰ Substituting the value in equation 1

$\rightarrow \qquad \tt 2x - y = - 4$

$\rightarrow \qquad \tt 2( 3 ) - y = - 4$

$\rightarrow \qquad \tt 6 - y = - 4$

$\rightarrow \qquad \tt {\purple{\boxed{\frak{y = 10 }}}\blue\bigstar}$

Therefore:

• ${\purple{\underline{\boxed{\frak{ Original \; Fraction = \dfrac{3}{10} }}}\bigstar}}$

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