If unity is subtracted from the numerator of a certain fraction, and 2 is added to the denominator, it reduces to 2/3; if 3 is added to the numerator, and the denominator is multiplied by 2, it reduces to 3/5. What is the fraction?
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Step-by-step explanation:
Let the numerator be x and the denominator be y.
From the given information, we have,
yx+2=21andy−1x=31or,yx+2=21=>2(x+2)=y=>y=2x+4....(i)Also,y−1x=31=>3x=y−1....(ii)
Using substitution method,
Substituting equation (i) in equation (ii), we get,
3x=2x+4−1=>x=3
Substituting x=3 in equation (i), we get,
y=2x+4=>y=2(3)+4=>y=6+4=>y=10
Thus, the original fraction is yx=103
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