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

Let unit’s digit = y

and the ten’s digit = x

So, the original number = 10x + y

The sum of the two digit number = 10x + y

The sum of the digit = x + y

According to the question,

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

10x + y = 4x + 4y

10x – 4x + y – 4y = 0

6x – 3y = 0

2x – y = 0

y = 2x …(i)

After interchanging the digits, New number = x + 10y

and 10x + y + 18 = x + 10y

10x + y + 18 = x + 10y

10x – x + y – 10y = – 18

9x – 9y = – 18

x – y = – 2 …(ii)

On substituting the value of y = 2x in Eq. (ii), we get

x – y = – 18

x – 2x = – 2

– x = – 2

x = 2

On putting the value of x = 2 in Eq. (i), we get

y = 2×2 = 4

So, the Original number = 10x + y

= 10×2 + 4

= 20 + 4

= 24

Hence, the two digit number is 24.

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