Q. 283.7( 7 Votes )

# The numerator of a fraction is one less than its denominator. If 3 is added to each of the numerator and denominator, the fraction is increased by 3/28, find the fraction. 28

Answer :

Let the denominator = x

Given that numerator is one less than the denominator

⇒ numerator = x – 1

So, the fraction

According to the question,

⇒ 28{(x^{2} + 2x) – (x^{2} –x + 3x – 3)} = 3 (x^{2} + 3x)

⇒ 28x^{2} + 56x – 28x^{2} – 56x + 84 = 3x^{2} + 9x

⇒ 3x^{2} + 9x – 84 = 0

⇒ x^{2} + 3x – 28 = 0

⇒ x^{2} + 7x – 4x – 28 = 0

⇒ x(x + 7) – 4(x + 7) = 0

⇒ (x – 4) (x + 7) = 0

⇒ x = 4 and – 7

But x is a natural number

Hence, x = 4

So, the fraction is

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