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A number consist of two digit whose sum is 10. If the digits of the number are reversed, then the number decreased by 36. Which of the following is/are correct?
I. The number is divisible by a composite number.
II. The number is multiple of a prime number.
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- Only I
- Only II
- Both I and II
- neither I nor II
- Only I
Correct Option: B
Let the two digit number be 10x + y.
Now, according to the question,
x + y = 10............(i)
if digits reversed , number get decreased by 36,
and ( x +10y) = ( 10x + y ) - 36
⇒ - 9y + 9x = 36
⇒ x - y = 4 ..................... (ii)
On adding Eqs. (i) and (ii), we get
2x = 14
⇒ x = 7
∴ x = 7 and y = 3
∴ Required number is 73.
So,the number is a multiple of a prime number.
