Question

The sum of the digits of a two- digit number is 9. If the number formed by reversing its digits is 27 less than the original number, find the original number

Answer 1

Let the no be 10 x +y

ATQ

x+y=9

10y+x+27= 10 x + y

x-y =3

Solving for x and y

We get x =6 and y =3

Therefore the no is 63

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Answer 2

Answer:

The 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?

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There is a simple test for divisibility by 9 that states a number is divisible by 9 if (and only if) the (repeated) digit sum of the number is divisible by 9. For example, 18 and 81 are divisible by 9 because 1+8=9.

So the two-digit number we are looking for is divisible by 9.

Moreover the difference to another number divisible by 9 is 27. For the majority of numbers (those ending in 4 and higher), adding 27 lowers the units place by 3 so I started thinking about those, and quickly found 36. But a more structured way is nothing that the two-digit multiples of nine pair up:

18 <=> 81

27 <=> 72

36 <=

Sum of the digits of a two -digit number is 9. The number obtained by interchanging the digits extends the given number by 27. Can you find the original number?

The sum of the digits of a two-digit number is 9. The number obtained by interchanging the digits exceeds the given number by 27. What is the given number?

One of the two digits of a two digit number is 3 times the other digit. If you interchange the digits of this two digit number and add the resulting number to the original number, you get 88. What is the original number?

The sum of two digits of a two digit number is 9. If the digits are interchanged, the new number formed is 9 more than the original number. What is the number?

The sum of two digit number is 9 by interchanging the place of the digit number is reduced by 63 find the original number?

Let the unit digit be y and tens digit be x

Number formed = 10x + y

Reverse number = 10y + x

x + y = 9 (Given)…………………………eq1

10y + x = 10x + y + 27…………………….eq2

9y - 9x = 27

y - x = 3……………………………………..eq3

Solving eq1 and eq3 ,we get

x = 3 and y = 6

Original Number = 36 Reversed Number = 63

You can crosscheck the answer by putting up the values obtained either in eq1 or eq2 or eq 3