Answer :

Let tens place digit be y and the units place be x.

∴ Our number is (10y + x)

Our given first condition is that our number is 3 more than 4 times the sum of its digits.

∴ By given condition,

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

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

6y - 3x = 3

3(2y - x) = 3

2y - x =1 …(1)

Our given second condition is that if 18 is added to the number, its digits are reversed.

The reversed number is (10x + y)

∴ By given condition,

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

10y - y + x -10x = -18

9y - 9x = -18

9(y - x) = -18

y - x = -2

y = x - 2 [2]

Putting this value of 'y' in eq (1), we have

2(x - 2) - x = 1

2x - 4 - x = 1

x = 5

From [2], we have

y = 5 - 2 = 3

y = 3 and x = 5

∴ Our number = (10 × 3 + 5) = 35

Hence, our number is 35.

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