A number consist of two digit whose sum is 10 If the digit of the number are reversed then the number decreased by 36. Which of the following is correct. I. The number is divisible by a composite number. II. The number is a multiple of a prime number.

only I
only II
Both I and II
Neither I nor II

Correct Answer: only II

Explanation:

let the two-digit number be 10p + q
Now according to the question
p + q = 10
and (p +10q) + 36 = (q + 10p)
⇒ -9q + 9p = 36
⇒ -q + p = 4 ....(ii)
on adding eq (i) and (ii) we get
2p = 14 ⇒ p =7
∴ p = 7 and q = 4
∴ Required number is the 73
So, the number is a multiple of prime number.

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