Question

4. A number consists of two digits whose sum is
When the digits are reversed, the number is 5
becomes greater by 9. Find the number​

Answer 1

Step-by-step explanation:

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A number consists of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.

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ANSWER

Let the digits in the tens be x and ones place be y.

Hence the number is 10x+y

By reversing 10y+x

Sum of digit =5

⇒x+y=5⟶(i)

Also that when 9 is added to the number the digits get interchanged.

∴(10x+y)+9=(10y+x)

10x+y+9=10y+x=0

9x−9y=−9

x−y=−1⟶(ii)

Adding (i) &(ii) we get , 

⇒x+y=5

⇒x−y=−1

⇒2x=4

⇒x=2

Put x=2 in x+y=5 

∴2+y=5

⇒y=3

Hence the no: is 23.

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Answer 2

Answer:

23

Step-by-step explanation:

Let the number be 10x +y x=ten's place , y = one's place

x + y = 5

---> [1]

reversed no: , 10y + x

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

X - y = -1

[2]

Adding equations 1 and 2

x + y = 5 X - y = -1

2x = 4

x = 2

X -y = -1

2-y= -1

2+1 = y

3=y

the number is :

10x + y

10 x 2 + 3

= 23

The no: is23