Q. 2

The denominator of a fraction is 1 more than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is1 : 2. Find the fraction.

Let the numerator be 'x' and denominator be 'y'

Given,

The denominator of a fraction is 1 more than twice its numerator

y =2 x + 1

⇒ y - 2 x = 1     ....... (1)

If 1 is added to numerator and denomination, the ratio of the numerator to denominator becomes 1:2.

2(x + 1) = y + 1

2x + 2 = y + 1

y - 2x = 1  ....... (2)

As (1) and (2) are the same, there can be infinitely many solutions for x and y.

One such solution is:

x = 4 and y = 9

Now,

y - 2 x = 9 - 2(4)
= 9 - 8
= 1

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