Question

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?​

Answer 1

QUESTION :- 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?

ANSWER :-

Since the number is a 3 digit number, number will be of the form $100 \times x + 10 \times y + z$.

Second digit is 4 times the third digit, $y = 4 \times z$

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.

[NOTE :- $x$ cannot be 0 because if $x = 0$, then it is a two digit number.]

So, $z$ can take values 1 and 2.

[NOTE :- $z$ cannot be 3 because 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 2

Answer:

Since the number is a 3 digit number, number will be of the form .

Second digit is 4 times the third digit,  

First digit is 3 less than the second digit,  

Therefore,  

Since  is a digit, it must lie between 1 and 9.

[NOTE :-  cannot be 0 because if , then it is a two digit number.]

So,  can take values 1 and 2.

[NOTE :-  cannot be 3 because if , then  will not be between 1 and 9.]

So, if  and . Therefore, the number is 141.

If  and . Therefore, the number is 582.

Therefore, the possible numbers are 141 and 582.

Step-by-step explanation:

thanks..