The following question has three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Find out the two-digit original number. I) The number obtained by interchanging the digits is 27 more than the original number II) Sum of both the digits is 13 III) Ratio of both the digits is 1 ∶ 1.6?

Option 4 : Any of two statements

Let the two digits be x and y

Considering statement I,

10x + y + 27 = 10y + x

⇒ 9x + 27 = 9y

⇒ 9 (y - x) = 27

⇒ y - x = 27/9

⇒ y - x = 3

This statement is not sufficient alone

Considering statement II,

x + y = 13

This statement is not sufficient alone

Considering statement III,

1.6x = y

Considering statement I and II together,

y - x = 3

⇒ y = 3 + x

x + y = 13

⇒ x + 3 + x = 13

⇒ 2x = 10

⇒ x = 5

y = 5 + 3 = 8

So, the number is 58

Statement I and II can answer the question

Considering statement I and III together,

y - x = 3

⇒ y = 3 + x

1.6x = y

⇒ 1.6x = 3 + x

⇒ 0.6x = 3

⇒ x = 3/0.6

⇒ x = 5

y = 5 + 3 = 8

So, the number is 58

Statement I and III can answer the question

Considering statement II and III together,

x + y = 13

⇒ y = 13 - x

1.6x = y

⇒ 1.6x = 13 - x

⇒ 2.6x = 13

⇒ x = 13/2.6

⇒ x = 5

y = 13 - 5 = 8

So, the number is 58

Statement II and III can answer the question