Question

A certain number of two digits
is three times the sum of its digits.
and if
45 be added to it, its
digits are reserved. Find the
number​

Answer 1

Let the ten's digit be x. The one's digit is y.

Given that a two digit number is 3 times the sum of its digits.

10x+y = 3(x + y)

10x + y = 3x + 3y

7x = 2y --- (1)

Given that if 45 is added to it, the digits are reversed.

10x + y = 10y - x - 45

9x = 9y - 45

x = y - 5 --- (2)

Substitute (2) in (1), we get

7(y-5) = 2y

7y - 35 = 2y

y = 7.

Substitute y = 7 in (2), we get

x = 7 - 5 =2.

The values of x and y are 72.

The number is 27.

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