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Eight times a two digit number is equal to three times the number obtained by reversing the order of its digits .if the difference between the digit is 5

,find the number.




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Let the number be  A B          its value is  10 A + B
Reverse of the number BA      it s value is  10 B  + A

given  8 * (10A +B) = 3 (10 B + A )
80 A + 8 B = 30 B + 3 A
77 A - 22 B =  0
7A - 2 B = 0            =>  2B =  7A

we know that B is between  0 and 9.    A is between 0 and 9
B and A are not zeros.

A has a factor 2  and B has a factor 7 for the above equation to be true. There is no other way.
There is only one such possibility :  A = 2  and  B = 7

The number is  27.     
To solve this we do not need the second data, that is, difference between the digits is 5.  This information is not needed.

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