# A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

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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