When the greater of 2 numbers is increased by 1 divides the sum of the numbers the result is 3/2.When the difference of these numbers is divided by the smaller the result is 1/2. Find the number. 

Asked by archana | 30th Jan, 2017, 09:04: PM

Expert Answer:

begin mathsize 16px style Let space the space larger space number space be space straight x space and space the space smaller space number space be space straight y.
According space to space the space first space condition comma
fraction numerator straight x plus straight y space over denominator straight x plus 1 end fraction equals 3 over 2
rightwards double arrow 2 left parenthesis straight x plus straight y space right parenthesis space equals space 3 left parenthesis straight x plus 1 right parenthesis
rightwards double arrow 2 straight x space plus space 2 straight y space equals space 3 straight x space plus space 3
rightwards double arrow straight x space minus space 2 straight y space equals negative 3 space space.... left parenthesis 1 right parenthesis
According space to space the space second space condition comma
fraction numerator straight x minus straight y space over denominator straight y end fraction equals 1 half
rightwards double arrow 2 left parenthesis straight x minus straight y right parenthesis equals straight y
rightwards double arrow 2 straight x minus 2 straight y equals straight y
rightwards double arrow 2 straight x equals 3 straight y space
rightwards double arrow straight x equals fraction numerator 3 straight y over denominator 2 end fraction space space.... left parenthesis 2 right parenthesis
Substituting space left parenthesis 2 right parenthesis space in space left parenthesis 1 right parenthesis comma space we space get
fraction numerator 3 straight y over denominator 2 end fraction space minus space 2 straight y space equals negative 3
rightwards double arrow 3 straight y minus 4 straight y equals negative 6
rightwards double arrow negative straight y equals negative 6
rightwards double arrow straight y equals 6
So comma space straight x equals fraction numerator 3 left parenthesis 6 right parenthesis over denominator 2 end fraction equals 9
Hence comma space the space larger space number space is space 9 space and space the space smaller space number space is space 6.
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Answered by Rebecca Fernandes | 31st Jan, 2017, 08:48: AM

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