A two-digit number is 3 more than 4 times the sum of its digits. If 18

1.	A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.
Answer» Let us consider, one’s digit of the two digit number = x and Ten’s digit = y The number is x + 10y By reversing the digits, One’s digit = y and ten’s digit = x The number is y + 10x Now, As per the statement, 4(x + y) + 3 = x + 10y 4x + 4y + 3 = x + 10y 3x – 6y = -3 x – 2y = -1 ……..(1) And, x + 10y + 18 = y + 10x 18 = y + 10x – x – 10y 9x – 9y = 18 x – y = 2 …(2) On subtracting (1) form (2) y = 3 Form (1): x = 2y – 1 = 2(3 ) – 1 = 5 Answer: Number = x + 10y = 5 + 10 (3) = 35

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

Answer»

Let us consider, one’s digit of the two digit number = x and

Ten’s digit = y

The number is x + 10y

By reversing the digits,

One’s digit = y and

ten’s digit = x

The number is y + 10x

Now, As per the statement,

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

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

3x – 6y = -3

x – 2y = -1 ……..(1)

And,

x + 10y + 18 = y + 10x

18 = y + 10x – x – 10y

9x – 9y = 18

x – y = 2 …(2)

On subtracting (1) form (2)

y = 3

Form (1): x = 2y – 1 = 2(3 ) – 1 = 5

Answer:

Number = x + 10y = 5 + 10 (3) = 35