Question

A number consists of two digit whose sum is 9. If 9 is subtracted from the number the digits
interchange their places. Find the number.
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Answer 1

Answer:

$54$

Step-by-step explanation:

$Let\ the\ first\ digit\ of\ the\ two\ digit\ number\ be\ a\\Let\ the\ second\ digit\ of\ the\ two\ digit\ number\ be\ b\\Hence,\\We\ are\ given\ that,\\a+b=9\\Hence,\\b=(9-a)\\As\ we\ know\ that,\\The\ original\ number\ containing\ 2-digits\ can\ be\ written\ as: 10a+b\\Hence,\\The\ original\ number=10a+(9-a)\\The\ original\ number=9a+9$

$Now,\\Lets\ consider\ the\ reversed\ number\ with\ the\ reversed\ digits\ of\ the\\ original\ number.\\Hence,\\Reversed\ number\ containing\ reversed\ digits\ can\ be\ written\ as:10b+a\\Hence,\\Reversed\ number=10b+a\\Reversed\ number=10(9-a)+a=90-10a+a=90-9a$

$Now,\\We\ are\ given\ that,\\Original\ Number-9=Reversed\ number\\Or,\\Original\ Number-Reversed\ number=9\\Hence,\\9a+9-(90-9a)=9\\9a+9-90+9a=9\\18a=90\\a=\frac{90}{18}=5$

$As\ a=5, b=(9-5)=4\\Hence,\\The\ original\ number=10a+b=10*5+4=50+4=54$