Question

The numerator of a fraction is 1 less than the denominator. If 3 is added to each of the numerator and denominator, the fraction is increased by 3/28. Find the fraction.

Answer 1

Let the numerator be x
and denominator be y
Therefore the fraction is x/y

A.T.Q.---
x+1=y. ……(i)
x+3/y+3=x/y+3/28. ……(ii)

On solving equations (i) and (ii)

x/y=-17/18

Answer 2

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Let the Denominator = x

numerator = (x-1)

fraction = numerator/denominator

Fraction = x-1/x

A.T.Q

x-1+3/x+3 = x-1/x + 3/28

x+2/x+3 = 28x - 28 + 3x/ 28x

28x(x+2) = (31x - 28)(x+3)

28x² + 56x = 31x² - 28x + 93x - 84

31x² - 28x² + 93x - 28x - 56x - 84

3x² + 9x - 84

[ Divide by 3]


x²+ 3x - 28

x²+ 7x - 4x - 28

x(x+7) -4(x+7)

(x-4) (x+7)

x = 4 or -7 [x is a natural number, x>0]

Hence , x= 4

Fraction = x-1/ x = 4-1 /4 = ¾

Hence, the fraction is 3/4

_________________________

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