# A two-digit numbe

Let the unit digit be 'x'

Let the digit at ten's place be 'y'

The original number will be 10y + x

Given, number is 3 more than 4 times the sum of its digits

10y + x = 4(x + y) + 3

10y + x = 4x + 4y + 3

6y - 3x = 3

2y - x = 1

x = 2y - 1 eq.[1]

Also,

If the digits are interchanged,

Reversed number will be = 10x + y

As, reversed number exceeds the original number by 18,

(10x + y) - (10y + x) = 18

10x + y - 10y - x = 18

9x - 9y = 18

x - y = 2

2y - 1 - y = 2 eq.[using 1]

y = 3

Using this in eq.[1]

x = 2(3) - 1 = 5

Hence the original number is 10y + x = 10(3) + 5 = 30 + 5 = 35.

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