Question

Question No: 3
The sum of the two digit number is 9. If 27 is added to it, the digits get reversed then the number is
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Answer 1

Answer:

The number is 36.

Step-by-step explanation:

Given :-

• The sum of the digits of a two digit number is 9.
• If 27 is added to it , the digits number get reserved.

To find :-

• The number.

Solution :-

Let the unit's digit of the number be y and the ten's digit of the number be x.

Then,

• The number = 10x+y

According to the 1st condition,

• The sum of the digits of a two digit number is 9.

x+y = 9

→ x = 9-y................(i)

According to the 2nd condition,

• If 27 is added to it , the digits number get reserved.

10x+y+27 = 10y+x

→ 10x-x = 10y-y-27

→ 9x = 9y-27

→ 9(9-y)=9y-27

→ 81-9y=9y-27

→ -9y-9y = -27-81

→ -18y = -108

→ y = -108/-18

→ y = 6

• Unit's digit = 6

Now put y= 6 in eq(i)

x = 9-y

→ x = 9-6

→ x = 3

Therefore,

• The number = 10×3+6 = 36

Answer 2

Step-by-step explanation:

Assume that the ten's digit number be x and one's digit number be y.

The sum of the two digit number is 9.

→ x + y = 9

→ x = 9 - y ..............(1)

If 27 is added to it, the digits get reversed.

• Original number = 10x + y
• Reversed number = 10y + x

As per given condition,

→ 10x + y + 27 = 10y + x

→ 10x + y - 10y - x = - 27

→ 9x - 9y = -27

→ x - y = - 3 .............(2)

Substitute value of x in (2)

→ 9 - y - y = -3

→ -2y = -12

→ y = 6

Substitute value of y in (1)

→ x = 9 - 6

→ x = 3

Hence, the original number is 36 and reversed number is 63.