The sum of the digits of a two digit number is 12. The number obtained by reversing its digits exceeds the given number by 18. Then the number is_____a)75b)25c)52d)57Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Answer

Let ,one is x & another is y,
x+y =12. 1
and
10y + x = 10x +y+18. 2
Now solve
solving 2
9(x-y)=18
x-y = 2. 3
adding 1&3
we get,
2x=14
so,x=7
putting X's value in 1
we get y= 5

Required ni:- 57

Answer

Let us assume x and y are the two digits of the number
Therefore, two-digit number is = 10x + y and the reversed number = 10y + x
Given:
x + y = 12
y = 12 – x (1)
Also given:
10y + x - 10x – y = 18
9y – 9x = 18
y – x = 2 (2)
Substitute the value of y from Equation 1 in Equation 2
12 – x – x = 2
12 – 2x = 2
2x = 10
x = 5
Therefore, y = 12 – x = 12 – 5 = 7
Therefore, the two-digit number is 10x + y = (10*5) + 7 = 57
Hope this helped...

Answer

Option D is correct...

Answer

Solution:

Let's assume the two-digit number as 10x + y, where x and y represent the tens and units digits, respectively.

Given:
The sum of the digits of the two-digit number is 12.
x + y = 12

The number obtained by reversing its digits exceeds the given number by 18.
(10y + x) - (10x + y) = 18
9y - 9x = 18
y - x = 2

Using the two equations, we can solve for x and y.

Solving the Equations:

We have the following equations:
x + y = 12
y - x = 2

Adding both equations, we get:
2y = 14
y = 7

Substituting the value of y in the equation x + y = 12, we get:
x + 7 = 12
x = 5

Therefore, the two-digit number is 10x + y = 10(5) + 7 = 57.

Hence, the correct answer is option D) 57.

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