Question

A two-digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

Answer 1

My Answer: 24

The number is AB(Here AB means 10A + B.).

If 18 is added to the number, the digits are reversed.

AB+18=BA --- 1

A two-digit number is 4 times the sum of its digits.

AB=4A+4B --- 2

Simplify equation 1.

Equation 1 --- $10A+B+18=10B+A$

$9A-9B=-18$

$A-B=-2$

$A=B-2$ --- 3

Simplify Equation 2.

Equation 2 --- $10A+B=4A+4B$

$6A=3B$

$2A=B$

Now substitute 3 in.

$2B-4=B$

$B=4$

Substitute into 3.

$A=2$

The number AB is 24.