Answer :

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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