a certain number of two digit is three times the sum of its digit and if 45 added to it the digit will be reversed find the number ?​

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Let the number be (10 x + y)

Then, 10 x + y = 3 * (x + y) (given)

Or, 10 x + y = 3 x + 3 y

Or, 10 x - 3 x = 3 y - y

Or, 7x = 2 y

Or, x = 2 y / 7 ( Eq. 1)

Also, 10 x + y + 45 = 10 y + x ( given)

Or, 10 x - x = 10 y - y - 45

Or, 9 x = 9 y - 45 ( Eq. 2)

Substituting the value of x from (Eq. 1) in (Eq. 2), we have:

9 * 2 y / 7 = 9 y - 45

Or, (9 y ) - (18 y / 7) = 45

Or, 63 y - 18 y = 315

Or, 45 y = 315

Or, y = 7

From (Eq. 1),

x = 2 * 7 / 7 = 2

So, the number is 10 x + y = (10 * 2) + 7 = (20 + 7) = 27

Answer

Check:

Sum of the digits = 2 + 7 = 9

9 * 3 = 27 ✓

Adding 45 to the number 27, we get 72. So, the digits get reversed.

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