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The sum of the digits of a two-digit number is 6. If the place of digits in this number is interchanged, then there is a difference of 18 between the new number and the first number thus obtained. Which of the following will be this number?
1. 60
2. 51
3. 42
4. 15

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Correct Answer - Option 3 : 42

Let the number be (10x + y), where 'x' is the digit at tens place and 'y' is the digit at ones place.

The total sum of the digits of any two-digit number is 6.

According to the question:

x + y = 6 __________ (1)

After interchanging the digits, the new number we get is 10y+x.

If the place of digits in this number is mutually changed, then there is a difference of 18 between the new number and the first number thus obtained.

According to question:

10x + y - (10y + x) = 18

⇒ 10x + y - 10y - x = 18

⇒  9x - 9y = 18

⇒  9 (x - y) = 18

⇒  x - y = 18 ÷ 9

⇒  x - y = 2

⇒  x = 2 + y

Putting the value of x in equation (1), we get:

2 + y + y = 6

⇒ 2y = 6 - 2

⇒  2y = 4

⇒  y = 4 ÷ 2

⇒  y = 2

So, x = 2 + 2 (As, x = 2 + y and y = 2)

⇒ x = 4

Therefore, the number is: 10 × 4 + 2

= 40 + 2

= 42

Hence, ‘42’ is the correct answer.

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