Question

The sum of the numeratar and denomainater od a fruction is greater by 1 then thrice the numrator if the numerator is decreased by 1. then the frqction reduces to 1/3 . find the fraction Answers​

Answer 1

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☞ Your Answer is $\sf \dfrac{3}{10}$

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$\huge\sf\blue{Given}$

✭ The sum of numerator and denominator of a fraction is greater than thrice the numerator by 12. If numerator is decreased by 1 then the fraction is 1/3.

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◈ The fraction?

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Let us Assume the numerator as n and the denominator as d

Now ,

Case 1

The sum of numerator and denominator of a fraction is greater than thrice the numerator by 12

So,

$\sf n + d = 3n + 12$

≫ $\sf d = 2n + 12\qquad-eq(1)$

Case 2

If numerator is decreased by 1 then the fraction is 1/3.

$\sf n + \dfrac{1}{d} = \dfrac{1}{3}$

≫ $\sf 3n + 3 = d\qquad-eq(2)$

Equating eq(1) and eq(2)

➝ $\sf 2n + 12 = 3n + 3$

➝ $\sf\green{ n = 9 }$

➝ $\sf d = 3 × 9 + 3$

➝ $\sf\red{d = 30}$

So finally the Fraction is,

»» $\sf\dfrac{9}{30}$

»» $\sf\orange{Fraction = \dfrac{3}{10}}$

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Answer 2

Answer:

Given :-

The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator is decreased by 1 then the fraction reduced to 1/3.

To Find :-

What is the fraction.

Solution :-

Let, the fraction be x/y

According to the question,

➣ The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator.

⇒ x + y = 3x + 1

⇒ y = 3x - x + 1

⇒ y = 2x + 1 .......... equation no (1)

➣ Denominator is decreased by 1 than the fraction reduced by 1/3.

⇒ x - 1/y = 1/3

⇒ 3(x - 1) = y

⇒ 3x - 3 = y

⇒ 3x - y = 3 ......... equation no (2)

➣ Now, putting the value of x from equation no (1) in equation no (2) we get,

⇒ 3x - y = 3

⇒ 3x - (2x + 1) = 3

⇒ 3x - 2x - 1 = 3

⇒ x = 3 + 1

➠ x = 4

➣ Again, putting the value of x in the equation no (1) we get,

⇒ y = 2x + 1

⇒ y = 2(4) + 1

⇒ y = 8 + 1

➥ y = 9

Hence, the required fraction will be,

↦ x/y

➽ 4/9

∴ The fraction will be 4/9 .