The sum of the digits of a two-digit number is 9. If 27 is added to it, the digit of number get reversed. The number isa)25b)72c)63d)36Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Lets,

First digit number = x

Second digit number = y

Number = (x+10y)

A/Q,

x + y = 9 ...................... (i)

A/Q,

(x+10y) = (10x+y) + 27

x + 10y = 10x + y +27

9x - 9y = 27

9(x - y) = 27

x - y = 27/9

x - y = 3 ......................... (ii)

Equation (i) and (ii) we get,

x = 3

Putting the value of x in eq.(i)

we get,

y = 6

Number = (10x +y)

= 10 x 3 + 6

= 30 + 6

= 36

Answer

Explanation:
Let the tens digit of the number be x and the unit digit be y.
So, the number can be written as 10x + y.
According to the question, the sum of the digits of the number is 9, so we have:
x + y = 9 ...(1)
Also, when 27 is added to this number, the digits are reversed. This means that:
10y + x + 27 = 10x + y
Simplifying this equation, we get:
9y - 9x = -27
y - x = -3 ...(2)
Now, we have two equations (1) and (2) with two variables (x and y).
We can solve these equations simultaneously to find the values of x and y.
Multiplying equation (1) by (-1), we get:
-x - y = -9
Adding this equation to equation (2), we get:
-2x = -12
x = 6
Substituting the value of x in equation (1), we get:
y = 3
Therefore, the number is 63, and the correct option is (d).

Answer

Answer

The possibilities are:
18, 27, 36, 45, 54, 63, 72, & 81.
A quick addition of 27 to each possibility gives
18+27= 45,
27+27=54,
36+27=63 and
63 is the reverse of 36.

Answer

Solution:
Let the tens digit be x and the units digit be y. Then the number is 10x + y.
The sum of digits is 9, so we have x + y = 9. (Equation 1)
When 27 is added to the number, the digits are reversed. This means that the new number is 10y + x. So we have:
10x + y + 27 = 10y + x (Equation 2)
Simplifying equation 2, we get:
9x - 9y = -27
Dividing both sides by 9, we get:
x - y = -3 (Equation 3)
Solving equations 1 and 3 simultaneously, we get:
x + y = 9
x - y = -3
Adding these two equations, we get:
2x = 6
x = 3
Substituting x = 3 in equation 1, we get:
y = 6
Therefore, the number is 10x + y = 30 + 6 = 36
Hence, option D is correct.

Answer

Maths

A number consists of two digits whose sum is 9. If 27 is added to the number, its digits are interchanged. Which of the given steps is CORRECT to find the number?
Step 1 : Let the units digit be x
Step 2 : Then, ten's digit = (9 - x)
herefore∴ Number = 10 x (9 - x) + x
\Rightarrow⇒ 90 - 10x + x = (90 - 9x)
Step 3 : Adding 27 to the number 90 - 9x, we get 117 - 9x
Step 4 : Number with digits interchanged is 10x + (9 - x) = 9x + 9
Step 5 : 117 - 9x = 9x + 9
Step 6 : Therefore unit's digit = 6 and ten's digit = 3
Step 7 : Hence the number = 36.

Answer

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