Question

21. A certain number between 10 and 100 is eight times the
sum of its digits,
and if 45 be subtracted from it the digits will be reversed: find the number.
Please answer. best answer will be marked Brainliest and followed.​

Answer 1

Question:-

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

Required Answer:-

Given:-

• The number is between 10 and 100
• The number is 8 times of the sum of its digits. (Condition 1)
• If 45 is subtracted from it, the digit will be reversed. (Condition 2)

To Find:-

• The number.

Solution:-

Let,

• The first digit be x
• Second digit be y

Hence,

• The number is = 10x + y

❏ According to the first condition:-

• 10x + y = 8(x + y)

• ⇒ 10x + y = 8x + 8y

• ⇒ 10x - 8x = 8y - y

• ⇒ 2x = 7y

• ∴ x = 7y/2 ------------------------- (1)

❏ According to the second condition:-

• 10x + y - 45 = 10y + x

• ⇒ 10x - x - 45 = 10y - y

• ⇒ 9x = 9y + 45

• ⇒ 9x - 9y = 45

• ⇒ 9 (x - y) = 45

• ∴ x - y = 5 ------------------------- (2)

❑ Putting the value of x equation 2:-

• 7y/2 - y = 5

• ⇒ 5y/2 = 5

• ∴ y = 2

❑ Again putting the value of y in equation 2:-

• x - 2 = 5

• ⇒ x = 5 + 2

• ∴ x = 7

Therefore, the number is = 10x + y = 10 × 7 + 2 = 72

Hence, the number is 72