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:

The original two digit number is 36.

Step-by-step explanation:

Let the unit's digit of the number be x

Therefore, Ten's digit will be 9-x

Hence, Number = (9-x)×10+x

= 90-10x+x = 90-9x

When we interchange the number,

New number = x×10+(9-x)

= 10x+9-x = 9x+9

By condition,

90-9x + 27 = 9x+9

=> 117 - 9x = 9x+9

=> 117-9 = 9x+9x

=> 18x = 108

=> x = 108/18 = 6

Original number = 90-9x = 90-54 = 36.

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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