Question

b) A two-digit number is three times the sum of its digits. If 45 is added to the number; its digits
are reversed. Find the number.
[4]​

Answer 1

Answer:

27

Step-by-step explanation:

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 2

Answer:

27

Step-by-Step Explanation:

Let the one's digit = x

Ten's digit = y

Number = 10y + x

Given, a two-digit number is three times the sum of its digits.

⇒ 10y + x = 3 (x + y)

⇒ 10y + x = 3x + 3y

⇒ 7y = 2x = 1

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

⇒ 10y + x + 45 = 10x + y

⇒ 9x − 9y = 45

⇒ x − y = 5

⇒ x = 5 + y = 2

Substituting 2 in 1, we get:

⇒ 7y = 2 (5 + y)

⇒ 7y = 10 + 2y

⇒ y = 2

So, x = 5 + 2 = 7

Hence, the required number is 27.

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