Question

a two digit number is 4 times the sum of its digit . if 18 is added to the number , the digits are reversed . find the number

Answer 1

Let unit's digit = x
Lrt ten's digit = y
Number = 10y + x
According to the question,
10y + x = 4(x + y)
10y + x = 4x + 4y
10y - 4y + x - 4x = 0
6y - 3x = 0
3(2y - x) = 0
2y - x = 0.........eq 1
10y + x + 18 = 10x + y
10y - y + x - 10x = - 18
9y - 9x = - 18
9(y - x) = - 18
y - x = - 18/9
y - x = - 2......... eq 2

1eq * 1 = 2y - x = 0
2eq * 2= 2y - 2x = - 4
- + +
___________________
x = 4
2y - 4 = 0
2y = 4
y = 4/2
= 2
Therefore,
The number = 24

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