• The denominator of a rational numbers is greater than its numerator by 3

• If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/3

• The original number

• Let the numerator be "n"

• Let the denominator be "d"

➠ ⚊⚊⚊⚊ (a)

The denominator of a rational numbers is greater than its numerator by 3

➜ d = n + 3 ⚊⚊⚊⚊ ⓵

➠ n - 3

➠ d + 2

Also given that , If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/3

So ,

➜

➜ 3n - 9 = d + 2 ⚊⚊⚊⚊ ⓶

⟮ Putting d = n + 3 from ⓵ to ⓶ ⟯

➜ 3n - 9 = n + 3 + 2

➜ 3n - n = 3 + 2 + 9

➜ 2n = 14

➜

➨ n = 7 ⚊⚊⚊⚊ ⓷

• Hence the numerator is 7

⟮ Putting n = 7 from ⓷ to ⓵ ⟯

➜ d = 7 + 3

➨ d = 10 ⚊⚊⚊⚊ ⓸

• Hence the denominator is 10

⟮ Putting equation ⓷ & ⓸ in equation (a) ⟯

➨

• Hence the original fraction

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