Question

A fraction became 1/3 when 2 is subtracted from a numerator and it becomes 1/2 when 1 is a subtracted from its denominator find the original fraction.

Answer 1

✬ Original Fraction = 7/15 ✬

Step-by-step explanation:

Given:

• Fraction becomes 1/3 when 2 is subtracted from numerator.
• Again it becomes 1/2 when 1 is subtracted from denominator.

To Find:

• What is the original fraction ?

Solution: Let the numerator be x and denominator be y. Therefore,

➯ Fraction = numerator/denominator

➯ Fraction = x/y

[ Subtracting 2 from the numerator ]

• New numerator = (x – 2)
• Fraction becomes = 1/3

➟ New numerator/denominator = 1/3

➟ (x – 2)/y = 1/3

➟ 3(x – 2) = y

➟ 3x – 6 = y.........(i)

[ Subtracting 1 from denominator ]

• New denominator = (y – 1)
• Fraction becomes = 1/2

➟ Numerator/new denominator = 1/2

➟ x/y – 1 = 1/2

➟ 2x = y – 1

{ Put the value of y here from equation 1)

➟ 2x = 3x – 6 – 1

➟ 2x – 3x = – 7

➟ – x = – 7

➟ x = 7

• Numerator is x = 7

{ Put the value of x in equation 1 }

➟ 3 × 7 – 6 = y

➟ 21 – 6 = y

➟ 15 = y

• Denominator is y = 15

Hence, original fraction is x/y = 7/15

Answer 2

Given:

• Fraction become 1/3 when 2 is subtracted from numerator
• Fraction become 1/2 when 1 is substrated from denominator

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Need to Find

• fraction=?

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Solution :

• Let the numerator be a
• denominator be b

Thus the fraction is $\bold{\purple{\dfrac{a}{b}}}$

As Given,

$\dfrac{a - 2}{b} = \dfrac{1}{3}$

By cross multiplying we get,

$\implies \: 3a - 6 = b \: - - - - i$

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Also,

$\dfrac{a}{b - 1} = \dfrac{1}{2}$

By cross multiplying,

$2a = b - 1 - - - - ii$

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Now by subtracting ii from i we get,

3a-6-2a= b -(b-1)

⟹ a - 6 = b-b +1

⟹ a = 1 + 6

⟹ $\purple{\boxed{\bold{a= 7}}}$

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Putting a = 7 in equation ii,

2 × 7 = b-1

⟹ b = 14 +1

⟹ $\purple{\boxed{\bold{b= 15}}}$

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Thus the fraction is $\bold{\red{\large{\boxed{\boxed{\frac{7}{15}}}}}}$