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Question

The numerator of a fraction is '3‘ less than its denominator if ’2‘ is added to both the numerator and denominator, then the sum of the new fraction and the original fraction is ’2920'. Find the original fraction.


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Solution

Let the denominator be 'x'.

Here, it is given that, the numerator is 3 less than the denominator, So, the numerator=x-3

The fraction=x-3x

It is given that if '2' is added to both the numerator and denominator, then the sum of the new fraction and the original fraction is 2920

Adding '2' to the numerator and denominator, the new fraction becomes, x-3+2x+2=x-1x+2

x-3x+x-1x+2=2920

x-3x+2+x-1xxx+2=292020x2+2x-3x-6+x2-x=29x2+2x202x2-2x-6=29x2+58x40x2-40x-120=29x2+58x11x2-98x-120=011x2-110x+12x-120=011x+12x-10=0

x=-1211 or x=10

Here, we will reject 'x=-1211'and will accept x=10

So, x-3x=710

Therefore, the original fraction is 710.


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