document.write( "Question 1159944: A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the digits are interchanged.What is the number? \n" ); document.write( "

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\n" ); document.write( "A two digit number is such that its value equals four times the sum of its digits.If 27 is added to the number the results is equal to the value of the number obtained when the digits are interchanged.What is the number?
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Let the tens and units digits be T, and U, respectively\r\n" );
document.write( "Then we get: 10T + U = 4(T + U)\r\n" );
document.write( "6T = 3U\r\n" );
document.write( "2T = U ------ eq (i)\r\n" );
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document.write( "Also, 10T + U + 27 = 10U + T\r\n" );
document.write( "10T - T + U - 10U = - 27\r\n" );
document.write( "9T - 9U = - 27\r\n" );
document.write( "9(T - U) = 9(- 3)\r\n" );
document.write( "T - U = - 3 ------ eq (ii)\r\n" );
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document.write( "T - 2T = - 3 ------ Substituting 2T for U in eq (ii)\r\n" );
document.write( "- T = - 3\r\n" );
document.write( "Tens digit, or \r\n" );
document.write( "2(3) = U ------ Substituting 3 for T in eq (i)\r\n" );
document.write( "Units digit or \r\n" );
document.write( "Number:

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