Question

The sum of numerator and denominator of a fraction is 30. If 2 is

added to numerator and 2 is subtracted from denominator, then it

becomes 2/3. Find the fraction.​

Answer 1

Answer:

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The sum of numerator and denominator of a fraction is 30. If 2 is added to numerator and 2 is subtracted from denominator, then it becomes 2/3.

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Fraction

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Let ,

• numerator be x
• denominator be y

So , fraction becomes x/y.

The sum of numerator and denominator of a fraction is 30

⇒ x + y = 30

⇒ x = 30 - y ... (1)

If 2 is added to numerator and 2 is subtracted from denominator , then it becomes 2/3

→ $\frac{x + 2}{y - 2} = \frac{2}{3}$

sub. (1) here ,

➡$\frac{(30 - y) + 2}{y - 2} = \frac{2}{3}$

➡$\frac{32 - y}{y - 2} = \frac{2}{3}$

➡ 3(32-y) = 2(y-2)

➡96- 3y = 2y - 4

➡ 5y = 100

➡ y= 20

Sub. y value in (1) ,

⇒ x = 30 - (20)

⇒ x = 10

So , Fraction is, $\frac{x}{y} = \frac{10}{20}$

Answer 2

Answer:

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