A 2 digits number is 8 times the sum of its digits, if 45 is subtracted from the number, its digit are reversed, what is the number?
A. 61
B. 65
C. 72
D. 84
Correct Answer: C
Explanation
Tens digit \(=x\)
Units digit \(=y\)
The number \(=10 x+y\)
The number when digits are reverse \(=10 y+x\)
\(10 x+y=8(x+y)\)
\(10 x+y=8 x+8 y\)
\(10 x-8 x+y-8 y=0\)
\(2 x-7 y=0 \ldots \ldots .(1)\)
\(10 x+y-45=10 y+x\)
\(10 x-x+y-10 y=45\)
\(9 x-9 y=45\)
\(9(x-y)=45\)ivide through by 5
\(x-y=5 \ldots \ldots . . .(2)\)rom eqn (2) \(x=5+y \ldots \ldots . .\) (3)
Put eqn (3) into eqn (1)
\(2(5+y)-7 y=0\) \(10+2 y \quad 7 y-0\) \(10-5 y=0, \quad 10=5 y\)ivide both sides by \(5, \quad y=2\)
Put \(y +2\) into eqn (3)
\(X =5+2=7\)
The number \(=10 x+y\)
\(10(7)+2=72 \quad\)