Q=if a three 3 digit units digit tense digit hundreds digit are in the ratio 1:2:3.if the difference of original number and the number obtained by reversing the digit is 594.find the no.
There are only three possibilities — 123, 246, 369. Which fits?
To solve this problem, let's break it down step by step:
Step 1: Understand the problem
We are given that the units digit, tens digit, and hundreds digit of a three-digit number are in the ratio 1:2:3.
Let's assume the units digit is x, the tens digit is 2x, and the hundreds digit is 3x.
Step 2: Form the original number
We can form the original number using the digits we have assumed. The original number would be: 100 * (3x) + 10 * (2x) + x = 300x + 20x + x = 321x.
Step 3: Reverse the digits
If we reverse the digits of the original number, we get a new number. Let's call this new number "reversed_number".
The reversed_number would be: 100 * x + 10 * (2x) + (3x) = 100x + 20x + 3x = 123x.
Step 4: Find the difference
The problem states that the difference between the original number and the reversed number is 594.
Therefore, the difference between the two numbers can be expressed as:
321x - 123x = 594.
Step 5: Solve the equation
Simplifying the equation:
198x = 594
Dividing both sides by 198:
x = 3.
Step 6: Find the original number
Now we can find the original number by substituting the value of x back into the original number expression:
Original number = 321 * x = 321 * 3 = 963.
So, the original number is 963.