Question

please solve it and step-by-step​

Answer 1

Given

The sum of digits of two-digit number = 9

If original number substracted from reversed number = 27

To find

Original number

Solution

Let the digit at unit's place be m & digit at ten's place be n.

➺ Original number = m + 10n

➺ Reversed number = n + 10m

According to 1st case :

➛ m + n = 9

➛ m = 9 - n -(Eq.1)

According to 2nd case :

➝ (n + 10m) - (m + 10n) = 27

➝ n + 10m - m - 10n = 27

➝ 9m - 9n = 27

➝ 9(m - n) = 27

➝ m - n = 27/9

➝ m - n = 3

• Putting value from (Eq.1)

➝ 9 - n - n = 3

➝ 9 - 2n = 3

➝ -2n = 3 - 9

➝ -2n = -6

➝ n = -6/-2

➝ n = 3

Now put this value in (Eq.1) :

➺ m = 9 - 3

➺ m = 6

Now finding the original number :

⟼ Original number = m + 10n

⟼ Original number = 6 + 10(3)

⟼ Original number = 6 + 30

⟼ Original number = 36

Therefore,

Original two-digit number = 36 .

Answer 2

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QUESTION :

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

It the number is subracted from the number formed by reversing the digits, the answer is 27.

Find the number.

SOLUTION :

Let the required number be 10 X + Y

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

Hence, we can derive the following equation :

X + Y = 9....... ( 1 )

Now,

Let us find the number formed by reversing the digits.

The number formed by reversing the digits of the original number is 10 Y + X

It the number is subracted from the number formed by reversing the digits, the answer is 27.

So,

10 Y + X - ( 10 X + Y ) = 27

=> 9 Y - 9 X = 27

=> Y - X = 3...... ( 2 )

Now add Equation (1) and Equation ( 2 )

So, we get the following result :

2 Y = 12

=> Y = 6

Substituting this value in either of the equations, we can find the value of X which comes out to be 6

So the required number becomes 6 3.

ANSWER :

The number is 63.