Question

Sum of the digits of 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 the two-digit number ?

Answer 1

Let the digits be x and y.

Then, x+y = 9

the original number is 10x+y.

On reversing, we get the new number as 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.

Thus, x = 3.Therefore, the original number is 36

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Answer 2

Given:

• Sum of two digit number = 9
• New number received when we interchange the digit is greater by = 27

To Find:

The two-digit number.

Solution:

Let the digit in tens place be x then digit in ones place will be (9 - x)

Original two digit number = $10x+(9-x)$

After interchanging the digits, the new number = $10(9-x)+x$

According to the question,

$10x+(9-x)+27=10(9-x)+x\\\implies 10x+9-x+27=90-10x+x\\\implies 9x+36=90-9x\\\implies 9x+9x=90-36\\\implies 18x=54$

Now, finding the value of x

$\implies x=\frac{54}{18} \\\implies x=3$

Original number = $10x+(9-x)=(10 \times 3)+(9-3)=30+6=\boxed{36}$

Thus, the number is 36