There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
Answers
Answer:
The possible three digit natural numbers satisfying the given conditions are 141 and 582.
Step-by-step-explanation:
Let the digit at hundreds place be x.
The digit at tens place be y.
And the digit at units place be z.
∴ Three digit number = xyz
⇒ Three digit number = 100x + 10y + z
From the first condition,
Tens digit = 4 * Units digit
⇒ y = 4z - - - ( 1 )
From the second condition,
Tens digit = Hundreds digit + 3
⇒ y = x + 3 - - - ( 2 )
From equations ( 1 ) & ( 2 )
⇒ 4z = x + 3
⇒ 4z - 3 = x
⇒ x = 4z - 3
Now,
Three digit number = 100x + 10y + z
⇒ Three digit number = 100 * ( 4z - 3 ) + 10 * 4z + z
⇒ Three digit number = 400z - 300 + 40z + z
⇒ Three digit number = 400z + 41z - 300
⇒ Three digit number = 441z - 300
Now,
If we substitute z = 0, the number becomes
441 * 0 - 300 = 0 - 300 = - 300
The number - 300 satisfies the given conditions, but it is not a natural number.
If we substitute z = 1, the number becomes,
441 * 1 - 300 = 441 - 300 = 141
The number 141 satisfies the given conditions.
If we substitute z = 2, the number becomes,
441 * 2 - 300 = 882 - 300 = 582
The number 582 satisfies the given conditions.
If we substitute z = 3, the number becomes,
441 * 3 - 300 = 1323 - 300 = 1023
As this number is four digit number, it's not acceptable.
∴ The possible three digit natural numbers satisfying the given conditions are 141 and 582.
Step-by-step explanation:
given :
- There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?
to find :
- What is the number?
solution :
- Since the number is a 3-digit number,number will be of the form 100*x+10*y+z
- Second digit is 4 times the third digit,y=4*z
- First digit is 3 less than the second digit,x=y-3
- Therefore,x=4*z-3
- Since x is a digit,it must lie between 1 and 9
- (x cannot be 0 coz if x=0,then it is a two digit number)
- So,z can take the values 1 and 2.
- ( z cannot be 3 coz if z=3,then y will not be between 1 and 9 )
- So if z=1,x = 1 and y=4 .Therefore , the number is 141
- If z=2,x=5 and y=8.Therefore, the number is 582.
- Therefore,the possible numbers are 141 and 582
answer:
- Therefore,the possible numbers are 141 and 582