Math, asked by pushpajio2016, 9 months ago

The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9.
What is the number?​

Answers

Answered by HarshChaudhary0706
1

Answer:

Let the first digit be  

a

Let the second digit be  

b

The first condition

a

+

b

=

7

...............................(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The second condition

The first order value:  

×

×

a

is a counting in tens. So actual value is  

10

×

a

×

×

b

is counting in units. So actual value is  

1

×

b

The first Order Value

=

10

a

+

b

...............................(2)

'-----------------------------------------------------------------------'

The second order value:

×

×

b

is a counting in tens. So actual value is  

10

×

b

×

×

a

is counting in units. So actual value is  

1

×

a

The second Order Value

=

10

b

+

a

.........................(3)

'----------------------------------------------------------------------'

From the question

Equation (3)

Equation (2)

=

9

.................................(4)

|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Putting it all together

Equation 4 becomes

(

10

b

+

a

)

(

10

a

+

b

)

=

9

9

b

9

a

=

9

.

.

...

...

...

...

...

...

...

...

...

...

...

...

...

...

.

.

(

4

a

)

a

+

b

=

7

.

.

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

.

(

1

)

From equation (1)

a

=

7

b

Substitute in  

(

4

a

)

giving:

9

b

9

(

7

b

)

=

9

9

b

+

9

b

63

=

9

18

b

=

72

b

=

72

18

=

4

Substitute in Equation (1) giving

a

+

b

=

7

a

+

4

=

7

a

=

3

Step-by-step explanation:

Let the first digit be  

a

Let the second digit be  

b

The first condition

a

+

b

=

7

...............................(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The second condition

The first order value:  

×

×

a

is a counting in tens. So actual value is  

10

×

a

×

×

b

is counting in units. So actual value is  

1

×

b

The first Order Value

=

10

a

+

b

...............................(2)

'-----------------------------------------------------------------------'

The second order value:

×

×

b

is a counting in tens. So actual value is  

10

×

b

×

×

a

is counting in units. So actual value is  

1

×

a

The second Order Value

=

10

b

+

a

.........................(3)

'----------------------------------------------------------------------'

From the question

Equation (3)

Equation (2)

=

9

.................................(4)

|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Putting it all together

Equation 4 becomes

(

10

b

+

a

)

(

10

a

+

b

)

=

9

9

b

9

a

=

9

.

.

...

...

...

...

...

...

...

...

...

...

...

...

...

...

.

.

(

4

a

)

a

+

b

=

7

.

.

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

...

.

(

1

)

From equation (1)

a

=

7

b

Substitute in  

(

4

a

)

giving:

9

b

9

(

7

b

)

=

9

9

b

+

9

b

63

=

9

18

b

=

72

b

=

72

18

=

4

Substitute in Equation (1) giving

a

+

b

=

7

a

+

4

=

7

a

=

3

Answered by amrishkumar0206
1
The number is 34
3+4=7
Reversing 34 is 43
34 is increased by 9 I.e 34+9=43
Hope it satisfies you.
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