Question

pls answer as early as possible. I will mark as brainliest

Answer 1

Answer:

153

Step-by-step explanation:

Let the hundredth, tenth and ones digit of the number be x,y,z.

(i) Original:

It can be represented as 100x + 10y + z.

Given that a three digit number is equal to 17 times the sum of its digits.

⇒ 100x + 10y + z = 17(x + y + z)

⇒ 100x + 10y + z = 17x + 17y + 17z

⇒ 83x - 7y - 16z = 0

(ii) Reversing:

It can be represented as 100z + 10y + x

Given that if 198 is added, the digits gets reversed.

⇒ 100x + 10y + z + 198 = 100z + 10y + x

⇒ 99z - 99x = 198

⇒ z - x = 2

⇒ z = x + 2

(iii) Sum of first and third digit:

According to the given condition,

⇒ x + z = y - 1

Substitute (ii) in (iii), we get

x + x + 2 = y - 1

2x + 2 = y - 1

y = 2x + 3

Substitute y = 2x + 3 & z = x + 2 in (i), we get

⇒ 83x - 7(2x + 3) - 16(x + 2) = 0

⇒ 83x - 14x - 21 - 16x - 32 = 0

⇒ 53x = 53

⇒ x = 1

Substitute x = 1 in (ii), we get

⇒ z = x + 2

⇒ z = 3.

Substitute x = 1, z = 3 in (iii), we get

x + z = y - 1

⇒ 1 + 3 = y - 1

⇒ 4 = y - 1

⇒ y = 5

Therefore, the required number is 153.

Hope it helps!