Question

the denominator of a fraction is bigger than its numerator by 3.if 3 is subtracted from the numerator and 2added to the denominator the value of fraction we get is 1/5.find the original fraction​

Answer 1

Answer:

Original fraction:

Let n= x

d= x + 3

numerator/denominator= x / x + 3

Obtained fraction:

x - 3/ x + 3 + 2 = 1/5

x - 3/ x + 5 = 1 /5

Then cross multiply,

5 (x-3) = 1 (x+5)

5x-15 = x + 5

5x - x = 5+15

4x = 20

x = 20/4

x=5

The value of the

Numerator= x = 5

Denominator = x+3 = 5+3 = 8

Numerator/Denominator = 5/8

Answer 2

Correct question:

The denominator of a fraction is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the value of fraction we get is $\sf {\dfrac {1}{5}}$. Find the original fraction.

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☆Answer☆

Given:

• Denominator of the fraction is greater than the numerator by 3.
• If 3 is subtracted from the numerator and 2 is added to the denominator, the value of fraction we get is $\sf {\dfrac {1}{5}}$

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To find:

• The original fraction.

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Solution:

• Let the numerator be x.
• Let the denominator be (x+3).

$\sf\dfrac{x - 3}{(x + 3) + 2} = \dfrac{1}{5}$

$\sf\dfrac{x - 3}{x + 3+ 2} = \dfrac{1}{5}$

$\sf\dfrac{x - 3}{x + 5} = \dfrac{1}{5}$

$\bigstar {\sf {\pink {Cross\ multiplication}}}$

5 (x-3) = x+5

5x - 15 = x+5

5x-x = 5+15

4x = 20

$\sf x = \dfrac {20}{4}$

$\boxed {\bf {\orange {x=5}}}$

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Verification:

Substitute the value of x as 5 in the equation,

$\sf\dfrac{5 - 3}{(5 + 3) + 2} = \dfrac{1}{5}$

$\sf\dfrac{2}{8+ 2} = \dfrac{1}{5}$

$\sf\dfrac{2}{10} = \dfrac{1}{5}$

$\sf\dfrac{1}{5} = \dfrac{1}{5}$

LHS = RHS

Hence Verified!

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The original fraction:

• Numerator = x

= 5

• Denominator = (x+3)

= (5+3)

= 8

$\boxed {\sf {\purple {The\ original\ fraction\ is\ \dfrac {5}{8}.}}}$