Question

Sum of the digits of a two-digit number is 9.when we interchange the digits, it is found that the resulting number is greater than 27.what is the two digit number

Answer 1

Given:

• Sum of a two digit number is 9.
• On interchanging the digits , the resulting number is greater than the original number by 27.

To Find:

• The original number.

Answer:

According to first statement,

Sum of a two digit number is 9.

So , Let us take , the

• Unit digit be x .
• Tens digit be (9-x).

So , the original number = 10(9-x) + x .

$\rule{200}5$

According to second condition ,

• On interchanging the digits the reversed number is greater than original number by 27 .

So , the reversed number = 10x + 9-x = 9x+9.

Atq ,

$\sf{\implies 10(9-x)+x +27 = 9x + 9}$

$\sf{\implies 90 - 10x + x +27 =9x +9}$

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

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

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

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

$\underline{\boxed{\red{\sf{\leadsto x =6}}}}$

Hence , we got ,

• Units digit = x = 6
• Tens digit = 9-x = 3 .

Hence the original number is 10×3+6 = 36.

Answer 2

$\mathfrak{\huge{\underline{\underline{\red{Question\:?}}}}}$

✳ Sum of the digits of a two-digit number is 9.when we interchange the digits, it is found that the resulting number is greater than 27.what is the two digit number.

$\mathcal{\huge{\fbox{\green{AnSwEr:-}}}}$

✒ The two digit number is 36 .

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Let the digits be x and y.

▶ x+y = 9

So, the original number = 10x+y.

On reversing,

we get the new number = 10y+x

The new number is greater than the old number by 27, i.e.

➡ (10y+x) - (10x+y) = 27

or 9y-9x = 27, or y-x = 3

and x+y = 9

Adding the two equations,

we get 2y = 12 or y = 6.

Thus, x = 3.

➡ Hence , the original number is 36.

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