The sum of a numerator and denominator of a fraction is 18. If the denominator increased by 2, the fraction reduces to 1/3. Find the fraction.

Sum of the numerator and denominator = 18

If the denominator is increased by 2 , the fraction reduces to 1/3.

the fraction

Let the fraction be x/y.

⟹ x + y = 18

⟹ x = 18 - y -- equation (1)

And,

If the denominator is increased by 2 , the fraction reduces to 1/3.

⟹ x/y + 2 = 1/3

⟹ 3x = y + 2

Substitute the value of x from equation (1).

⟹ 3(18 - y) = y + 2

⟹ 54 - 3y = y + 2

⟹ 54 - 2 = y + 3y

⟹ 52 = 4y

⟹ 52/4 = y

⟹ 13 = y

Substitute the value of y in equation (1).

⟹ x = 18 - 13

⟹ x = 5

Therefore, the required fraction x/y is 5/13.

I hope it will help you.

Regards.

step-by-step explanation:

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