Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?​

Answer 1

Answer:

Answer Expert Verified

The new number is greater than the old number by 27, i.e. Adding the two equations, we get 2y = 12 or y = 6. Thus, x = 3. Therefore, the original number is 36.

Answer 2

Answer:

• The two-digit number is 36.

Step-by-step explanation:

Given that:

• Sum of the digits of a two-digit number is 9.
• When we reverse the digits, it is greater than the original number by 27.

To Find:

• The two-digit number.

Let us assume:

• Let the digit at the units place be x.

Then,

• Digit at the tens place will be (9 - x).

And, the number is:

= 10(9 - x) + 1(x)

= 90 - 10x + x

= 90 - 9x

After reversing the digits:

• Digit at ones place is (9 - x).
• Digit at tens place is x.

And, the number is:

= 10(x) + 1(9 - x)

= 10 + 9 - x

= 9x + 9

Now, according to the question:

$\sf{\implies(9x + 9) - (90 - 9x) = 27}$

Opening the brackets,

$\sf{\implies9x + 9 - 90 + 9x = 27}$

Solving further,

$\sf{\implies18x-81 = 27}$

Transposing 81 from LHS to RHS and changing its sign,

$\sf{\implies18x = 27+81}$

Adding the numbers,

$\sf{\implies18x= 108}$

Transposing 18 from LHS to RHS and changing its sign,

$\sf{\implies x=\dfrac{108}{18}}$

Dividing the numbers,

$\sf{\implies x=6}$

Hence,

• x = 6

Therefore,

• Digit at the ones place = x = 6
• Digit at the tens place = (9 - x) = (9 - 6) = 3

And,

• The number is 36.