Question

Product of digits of a 2digit number is 35.The average of the number and the number formed by reversing the order is 66 . Find the number ?

Answer 1

Answer: 75 or 57

Step-by-step explanation:

If x and y are digits at tens and ones place respectively,

the number is 10x + y

Also, xy= 35 ...............(1)

After reversing the order, the number is 10y + x

According to the question,

     [ (10x + y) + (10y + x) ] / 2 = 66

⇒   11x + 11y = 132

⇒   x + y = 12

⇒   x = 12 - y ...............(2)

From eqn (1) and (2),

     (12 - y) y = 35

⇒   12y - y² = 35

⇒   y² - 12y + 35 = 0

⇒   y² - 5y - 7y + 35 = 0

⇒   (y - 5) (y - 7) = 0

⇒   y = 5 or y = 7 ..............(3)

From (2) and (3),

either x = 7 and y = 5, or x = 5 and y = 7.

Thus, the number is either 75 or 57.