Question

1.     The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99. Find the original number.​

Answer 1

Given -

The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, we get 99.

To find -

• Original number

Solution -

Let the tens digit be x and the ones digit be y

• Original number = 10x + y

✰ According to the first condition ✰

• The digits of a 2-digit number differ by 5.

→ x - y = 5 ----(i)

✰ According to the second condition ✰

• If the digits are interchanged and the resulting number is added to the original number, we get 99.

• Reversed number = 10y + x

→ 10x + y + 10y + x = 99

→ 11x + 11y = 99

→ 11(x + y) = 99

→ x + y = 9 ----(ii)

Add both the equations

→ (x - y) + (x + y) = 5 + 9

→ x - y + x + y = 14

→ 2x = 14

→ x = 7

Put the value of x in eqⁿ (ii)

→ x + y = 9

→ 7 + y = 9

→ y = 9 - 7

→ y = 2

•°• Original number = 10x + y = 72

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Answer 2

Answer:

Given :-

• The digits of a 2 digits number differ by 5. If the digits are interchanged and the resulting number is added to the original number we get 99.

To Find :-

• What is the original number.

Solution :-

Let, the digits at units place be x

And, the digits at tens place be x + 5

Then, the original number will be 10(x + 5) + x

Now, by interchanging the digits, we get a new number is 10x + (x + 5)

According to the question,

⇒ 10(x + 5) + x + 10x + (x + 5) = 99

⇒ 10x + 50 + x + 10x + x + 5 = 99

⇒ 10x + x + 10x + x + 50 + 5 = 99

⇒ 22x + 55 = 99

⇒ 22x = 99 - 55

⇒ 22x = 44

⇒ x = 44/22

➠ x = 2

Hence, the required digits are,

✧ Unit place = x = 2

✧ Tens place = x + 5 = 2 + 5 = 7

Hence, the required original number is 72

∴ The original number is 72 .