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A two digit number is obtained by multiplying the sum of digits by 8. Also it is obtained by multiplying the difference of digits by 14 and adding 2 . Find the number.

Asked by archana 30th January 2017, 8:58 PM
Answered by Expert
Answer:
begin mathsize 16px style Let space the space two space digit space number space be space 10 straight x space plus space straight y. space space
Two space digit space number space is space obtained space by space multiplying space sum space of space the space digits space by space 8 space
rightwards double arrow space 10 straight x space plus space straight y space equals space 8 left parenthesis straight x space plus space straight y right parenthesis space space
rightwards double arrow space 2 straight x space equals space 7 straight y space space space..... space left parenthesis 1 right parenthesis space space
Two space digit space number space is space obtained space by space multiplying space the space difference space of space the space digits space by space 14 space and space adding space 2 space space
rightwards double arrow 10 straight x space plus space straight y space equals space 14 left parenthesis straight x space minus space straight y right parenthesis space plus space 2 space space
rightwards double arrow space 2 straight x space minus space 15 straight y space equals space minus 2 space....... left parenthesis 2 right parenthesis space space
Solving space equations space 1 space space and space 2 comma space we space get space
7 straight y space minus space 15 straight y space equals space minus 2
rightwards double arrow negative 8 straight y equals negative 2
rightwards double arrow straight y equals 1 fourth
And space so comma space space 2 straight x space equals space 7 straight y rightwards double arrow space 2 straight x space equals space 7 open parentheses 1 fourth close parentheses rightwards double arrow straight x equals 7 over 8

bold NOTE bold colon bold space Kindly space check space the space numbers space in space the space question comma space cause space we space cannot space get space straight a space fractional space answer comma space
since space digits space cannot space be space in space terms space of space fractions.
However comma space this space is space the space method space to space solve space the space problem. space
The space final space answer comma space which space is space the space number space would space be space the space values space obtained space for space xy. end style
Answered by Expert 31st January 2017, 8:12 AM
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