Question

Sum of the digits of a two digit number is nine When we inter change 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:

Original Number = 36

Step-by-step explanation:

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.

Therefore, the original number is 36.

Answer 2

Original Number = 64

Step-by-step explanation:

Given:

Sum of a two digit number is 10.

After interchanging digits the new number formed is 18 less than original.

To Find:

What is the original number ?

Solution: Let the tens digit he x and ones digit be y. Therefore, number is 10x + y.

➟ Tens + Ones = 10

x + y = 10 or

x = (10 – y)......(1)

[ Now, interchanging the digits of the number ]

New number formed is 10y + x

A/q

After interchanging digits the new number formed is 18 less than original.

$\implies{\rm }$⟹ 10x + y = 10y + x – 18

$\implies{\rm }$⟹ 10x – x = 10y – y – 18

$\implies{\rm }$⟹ 9x = 9y – 18

$\implies{\rm }$⟹ 9x – 9y = – 18

$\implies{\rm }$⟹ 9(x – y) = – 18

$\implies{\rm }$⟹ x – y = 2

$\implies{\rm }$⟹ (10 – y) – y = 2

$\implies{\rm }$⟹ – 2y = 2 – 10

$\implies{\rm }$⟹ – 2y = – 8

$\implies{\rm }$⟹ y = 8/2 = 4

So, the digits of number is

• Ones digit is y = 4

• Tens digit is x = 10 – 4 = 6

Hence, the original number is 10(6) + 4 = 64