Q28 of 186 Page 4

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

Let the denominator = x

Given that numerator is one less than the denominator


⇒ numerator = x – 1


So, the fraction


According to the question,






⇒ 28{(x2 + 2x) – (x2 –x + 3x – 3)} = 3 (x2 + 3x)


⇒ 28x2 + 56x – 28x2 – 56x + 84 = 3x2 + 9x


⇒ 3x2 + 9x – 84 = 0


⇒ x2 + 3x – 28 = 0


⇒ x2 + 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


More from this chapter

All 186 →
26

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, then are in the ratio 2 : 3. Determine the fraction.

 27

The sum of the numerator and denominator of a fraction is 8. If 3 is added to both 3 the numerator and the denominator, the fraction becomes 3/4. Find the fraction.

 29

The age of the father is 3 years more than 3 times the son's age. 3 years here, the age of the father will be 10 years more than twice the age of the son. Find their present ages.

 30

Two years ago, a man was five times as old as his son. Two years later his age will be 8 more than three times the age of the son. Find the present ages of man and his son.