Question

the digits of a two digit number differ by 5 if the digit are interchanged and the resulting number is added to the orginal number we get 121 find the number​

Answer 1

AnswEr:-

Two digits number = 38

$\rule{200}{2}$

Solution:-

Let the digit at unit's place be y & digit at ten's place be z where y > z

∴ Two digit number = y + 10z

Case 1:-

⇒ y - z = 5

⇒ y = z + 5 [Eq.i]

Case 2:-

★ Interchanged number:-

⇒ New number = z + 10y

According to question:-

⇒ y + 10z + z + 10y = 121

⇒ 11y + 11z = 121

⇒ 11(y + z) = 121

⇒ y + z = 121/11

⇒ y + z = 11

⇒ y = 11 - z [Eq.ii]

Comparing both equations -

⇒ z + 5 = 11 - z

⇒ z + z = 11 - 5

⇒ 2z = 6

⇒ z = 6/2

⇒ z = 3

So, digit at ten's place = z = 3

Putting this value in (Eq.i)

⇒ y = 3 + 5

⇒ y = 8

So, digit at unit's place = y = 8

★ Two digit number:-

⇒ Number = 8 + 10(3)

⇒ Number = 8 + 30

⇒ Number = 38

Therefore,

$\therefore{\underline{\boxed{\textsf{Original two-digit number = {\textbf{38 }}}}}}$

Answer 2

Answer:

Given:

• The digits of a two digit number differ by 5 if the digit are interchanged and the resulting number is added to the orginal number we get 121.

Find:

• Find the number.

According to the question:

• Let us assume 'x' as the digit at units place and 'y' be the digit at ten's place.

We know that:

• Units place (>) Tens place [x > y].

Using formula:

⇒ Units place - Ten's place = 5

⇒ (x - y) = 5

⇒ x = (y + 5) - Equation (1)

Note:

• Sometimes when there a brackets between some number and that bracket means multiplication sign.

Finding the new number:

⇒ New number = (y + 10x).

⇒ [(x + 10y) + (y + 10x)] = 121

⇒ (11x + 11y) = 121

⇒ 11 (x + y) = 121

⇒ (x + y) = 121/11

⇒ (x + y) = 11

⇒ x = (11 - y) - Equation (2)

Comparing equation (1) & (2):

⇒ [(y + 5) = (11 - y)]

⇒ [(y + y) = (11 - 5)]

⇒ 2y = 6

⇒ y = 6/2

⇒ y = 3

Therefore, 3 is digit at ten's place.

Adding values to equation (1):

⇒ x = (3 + 5 = 8)

⇒ x = 8

Therefore, 8 is units place.

Now, let's find the 'number' using the values:

⇒ 8 + 10 (3)

⇒ 8 + 30

⇒ 38

Therefore, 38 is the original number.