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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 new fraction and original fraction is 29/20 . find the original fraction

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Solution

Let the numerator be x and denominator be y.
Then, fraction will be xy.
According to the question,
y=x+3 ...(i)
x+2y+2+xy=2920xy+2y+xy+2xy2+2y=29202xx+3+2x+3+2xx+32+2x+3=2920 From equation(i)2x2+6x+2x+6+2xx2+6x+9+2x+6=2920202x2+10x+6=29x2+8x+1540x2+200x+120=29x2+232x+43511x2-32x-315=011x+45x-7=0x=-4511, 7If x =-4511 then y=-4511+3=-1211 and fraction =4512 Which dose not satisfiy the condition given in the questionIf x =7 then y=7+3=10 and fraction =710.Hence, the original fraction =710

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