Question

The sum of the digits of a two digit number is 9 . If 27 is added to it the digits of the number get reversee. The number is?

Answer 1

Answer:

Step-by-step explanation:

Let the number be: ab

reversed number:ba

a+b=9......................equation 1

ab=10a+b

ba=10b+a

ab-ba=9a-9b

27=9(a-b)

3=a-b

a-b=3

a=3+b..........................equation 2

merging equation 1 and 2

a+b=9

3+b+b=9

3+2b=9

2b=6

b=3

a=3+b=3+3=6

hence the req. no. =63

Answer 2

✤ AnSwer:

• The number is 36.

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Assumption :

• Let the digit at unit's place be y similarly, the digit at ten's place be x.

Hence, the no. will be 10x+y.

★ According to the 1st condition :

$\implies$ x + y = 9---(1)

★ According to the 2nd condition :

$\implies$ 10y + x = 10x + y + 27

$\implies$ 9y = 9x + 27

$\implies$ y = x + 3---(2)

Put the value of y in (2), we have

$\implies$ x+x+3=9

$\implies$ x=3

Now, let us find value of y,

$\implies$ x+y=9

$\implies$ 3+y=9

$\implies$ y = 9 - 3

$\implies$ y = 6

So, the number is,

$\implies$ 10x + y

$\implies$ 10(3) + (6)

$\implies$ 30 + 6

$\implies$ 36

• Number = 36

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