Question

A natural number 75 times the average of its digits. Given that it is a 3 digit number. Find possible values of digits of the number.

Answer 1

Answer:

150 , 225 & 375 are the number

Step-by-step explanation:

Let say Number = XYZ

Average of Digits = (X + Y + Z)/3

Value of number = 100X  + 10 Y + Z

Number = 75 times Average

=> 100X  + 10 Y + Z = 75 * (X + Y + Z)/3

=> 100X + 10Y + Z = 25 ( X + Y + Z)

=> 100X + 10Y + Z = 25X + 25Y + 25Z

=> 75X = 15 Y + 24 Z

X can not be zero as its a 3 digit number

Let say

X = 1

=> 75 = 15 Y + 24 Z

=> Y = 5 & Z = 0

150  is the number

Let say

X = 2

=> 150 = 15 Y + 24 Z

=> Y = 2 & Z = 5

225  is the number

Let say

X = 3

=> 225 = 15 Y + 24 Z

=> Y = 7 & Z = 5

375  is the number

Let say

X = 4

=> 300 = 15 Y + 24 Z

no combination

15 Y + 24Z can be max = 15*9 + 24* 9 =  351

so x can not 5 or greater than 5

150 , 225 & 375 are the number