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?
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Correct Answer: Option 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 \(=10 x+y\)
\(10(7)+2=72 \quad\)
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 \(=10 x+y\)
\(10(7)+2=72 \quad\)