A natural number equals 75 times the average of its digits. How many 3 digit numbers satisfy this condition?
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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
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