The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements: 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct?

LohaHridoy
  1. 1 only
  2. 2 only
  3. Both 1 and 2
  4. Neither 1 nor 2

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AhmedNazir

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Option 2 : 2 only

Calculation:

Let us assume the number has y in units place and x in tens place.

So, the number can be written as 10x + y

Now,

if we interchange the digits ⇒ x in units place and y in tens place

The number obtained = 10y + x

As given in the question we can write

    (10x + y) - (10y + x) = 54

⇒ 9x - 9y = 54 = 9(x - y) = 54

⇒ x - y = 6

⇒ x = y + 6

Here y can't be 0 as after interchanging the digits the number formed will not be a 2-digit number. So the possible outcomes are

If y = 1, x = 7 and the numbers are 71 and 17

If y = 2, x = 8 and the numbers are 82 and 28

If y = 3, x = 9 and the numbers are 93 and 39

Statement 1 is incorrect as by knowing the products of digit is not the only way. If their ratios are given then also we can find the numbers.

Statement 2 is correct as the difference of the digits is obtained by the equation x - y = 6.

Hence, option 2 is correct.

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