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

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.

To find :-

What is the number?

Solution:-

Let the digit at 100's place in a 3-digit number be X

Then the value of X = 100×X = 100X

Let the digit at 10's place in the 3-digit number be Y

Then the value of Y = 10×Y = 10Y

Let the digit at 1's place in the 3-digit number be Z

Then the value of Z = Z×1 = Z

The 3-digit number = 100X+10Y+Z

Given that

The second digit is four times as big as the third digit

=> Second digit = 4×Third digit

=> Y = 4×Z

=> Y = 4Z --------------(1)

and

The first digit is three less than the second digit

=> First digit = Second digit -3

=> X = Y-3 ------------(2)

On Substituting the value of Y from (1) in (2) then

=> X = 4Z-3 ---------(3)

Put Z = 1 then X = 4(1)-3 = 4-3 = 1

Put Z = 2 then X = 4(2)-3 = 8-3 = 5

Put Z = 3 then X = 4(3)-3 = 12-3 = 9

Put Z = 4 then X = 4(4)-3 = 16-3 = 13

Since X,Y,Z are single digits then

The possible values of Xare 1,5,9

If Z = 1 then Y = 4(1) = 4

If Z = 2 then Y = 4(2) = 8

If Z = 3 then Y = 4(3) = 12

Since X,Y,Z are single digits then

The possible values of Y are 4,8

Now we have ,

If Z = 1 then X = 1, Y = 4 then the number = 141

If Z = 2 then X = 5, Y = 8 then the number = 582

The possible numbers = 141 and 582

Answer:-

The required number for the given problem are 141 and 582

Note :-

Both the numbers satisfies the given data.

Check :-

Second digit = 4×Third digit

in 141 , 4 = 4×1 = 4

and

First digit = Second digit -3

=> 1 = 4-4 = 1

Verified

and

Second digit = 4×Third digit

in 582 , 8= 4×2 = 8

and

First digit = Second digit -3

=> 5 = 8-3 = 5

Verified the given relations in the given problem.