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Question
The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent with `1/2`. Find the fraction.
Solution
Let the numerator of the fraction be x.
∴ Denominator = x + 12
∴ The fraction = `"x"/("x" + 12)`
If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction obtained is `1/2`.
From the given information,
`("x" - 2)/("x" + 12 + 7) = 1/2`
⇒ 2 (x − 2) = 1 ( x + 12 + 7)
⇒ 2x − 4 = x + 19
⇒ 2x − x = 19 + 4
⇒ x = 23
∴ Numerator of the fraction is 23.
∴ Denominator of the fraction is 23 + 12 = 35.
Hence, the fraction is `23/35`.
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