The digit in the hundreds place of a three-digit number is 3 times the digit in the units place; the digit in its tens place is twice the digit in the units place. If the sum of all the three digit is 12,find the number
Answers
Step-by-step explanation:
Given :-
The digit in the hundreds place of a three-digit number is 3 times the digit in the units place; the digit in its tens place is twice the digit in the units place.The sum of all the three digit is 12.
To find :-
Find the number ?
Solution :-
Let the unit digit of a three digits number be Z
Place value of Z = Z×1 = Z
Let the digit at tens place in the three digits number = Y
The place value of Y = 10×Y = 10Y
Let the digit at hundreds palce in the three digits number = X
The place value of X = 100×X = 100X
The three digits number = 100X+10Y+Z
Given that
The digit in the hundreds place of a three-digit number is 3 times the digit in the units place
=> X = 3Z ------------(1)
and
The digit in its tens place is twice the digit in the units place.
=> Y = 2Z ------------(2)
and
The sum of all the three digit is 12.
=> X + Y + Z = 12 --------(3)
On Substituting the values of X and Y in (3)
=> 3Z + 2Z + Z = 12
=> 6Z = 12
=> Z = 12/6
=> Z = 2
The digit at unit's place = 2
On Substituting the value of Z in (1)
X = 3×2 = 6
The digit at hundreds place = 6
On Substituting the value of Z in (2)
Y = 2×2 = 4
The digit at tens place = 4
The three digits number = 100X+10Y+Z
=> 100(6)+10(4)+2
=> 600+40+2
=> 642
Answer:-
The three digits number for the given problem is 642
Check :-
The number = 642
Digit at hundreds place = 6
=> 3×2
=>3 times the digit at units place
Digit at tens place = 4
=> 2×2
=> Twice the digit at units place.
The sum of the digits = 6+4+2 = 12
Verified the given relations in the given problem.
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