Question

A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from it the digits will be reversed. Find the number.​

Answer 1

Answer:

72

Step-by-step explanation:

As number is between 10 and 100, it's a two digit number.

Let that two digit number be ab, where a is tens digit and b is unit digit.

As ab is two digit number it can be written as 10a + b.

So, number is 10a + b.

According to question:

= > number = 8 * sum of digits

= > 10a + b = 8( a + b )

= > 10a + b = 8a + 8b

= > 2a = 7b

= > a = (7/2) b ... (1)

Also, if 45 is subtracted, it's reversed so new number becomes "ba" that can be written as 10b + a.

= > original number - 45 = new number

= > 10a + b - 45 = 10b + a

= > 9a - 9b = 45

= > a - b = 5

= > (7/2) b - b = 5 { from (1)}

= > (5/2)b = 5

= > b = (2*5)/5

= > b = 2

Hence,

a = (7/2) b = (7/2) * 2 = 7

Hence the number is ab = 72