Question

the denominator of a rational number is greater than its numerator if 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 by 5 find the original number​

Answer 1

Correct Question :-

• The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from numerator 2 is added to its denominator the new no. becomes  1/5, Find original number.

Solution :-  

~Here, we’re given that  denominator of a rational number is greater than its numerator by 3 , If 3 is subtracted from numerator 2 is added to its denominator the new no. becomes 1/5 and we need to find the original fraction. Firstly we’ll assume the numerator and write the denominator accordingly and then we’ll form an equation according to the question. After solving that equation we’ll get the original fraction.

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》Let the numerator be ‘ x ’

》Then denominator will be ‘ x + 3 ’

According to the question :-

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

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

$\sf \dashrightarrow 1( x + 5 ) = 5( x -3 )$

$\sf \dashrightarrow x + 5 = 5x -15$

$\sf \dashrightarrow 5x-x = 15 + 5$

$\sf \dashrightarrow 4x = 20$

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

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

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Hence,  

• The original fraction is 5/8

Verification :-

~We can verify our answer by putting the values in the condition given to us in the question.  

$\sf \dashrightarrow \dfrac{5-3}{8+2} = \dfrac{1}{5}$

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

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

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

$\boxed{\bf{ \star \;\; LHS = RHS }}$

Hence, Verified

Answer 2

Given:-

• The denominator of a rational number is greater than its numerator if 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 by 5.

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To find:-

• The original number.

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Solution:-

Let,

• the numerator be x.
• the denominator be x + 3.

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According to the question,

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⇢ x - 3/x + 3 + 2 = 1/5

⇢ x - 3/x + 5 = 1/5

⇢ 1(x + 5) = 5(x - 3)

⇢ x + 5 = 5x - 15

⇢ 5x - x = 15 + 5

⇢ 4x = 20

⇢ x = 20/4

⇢ x = 5

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Hence,

• The original number is 5.