Linear Equations in Two variables

Question

If a two digit number is divided by the sum of its digits the quotient is 9. But the number obtained by reducing the digit at the tens place by the four times the digit at unit's place , leaves the remainder 5 when divided by the the sum of the digits of the original number.Find the original number.

 

Answer is 81 

Answer 1

Yes, 81 is correct.

(10T + U)/(T + U) = 9

10T + U = 9T + 9U

T = 8U and under the conditions of the problem only U=1 and T=8 satisfies the problem.

 

Then 8-4=4, 41/9 = 4 with remainder 5