Question

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

Let the digit in ten's. Place be x and the digit in the one's place be y.
∴x−y=5⟶(i)
∴ Two digit number=10x+y
Two digit after reversing the digits=10y+x
According to question ,
∴10x+y+10y+x=99
⇒11x+11y=99
⇒x+y=9⟶(ii)
On adding (i) and (ii),
2x=14
⇒x=7
Putting the value of x in equation (i)
x−y=5
⇒y=2
∴ Number=10x+y
=72.

Answer 2

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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