the difference b/w a 3 digit number and the number formed by reversing its digits is 396,the difference of hundreds and the units digit,is one less than the sum of the units and tens digit .find the number
To solve this problem, let's break it down step by step:
Step 1: Let's assume the number in question has three digits and can be written as "ABC", where A represents the hundreds digit, B represents the tens digit, and C represents the units digit.
Step 2: We know that the difference between the number "ABC" and the number formed by reversing its digits "CBA" is 396. Mathematically, we can express this as:
(100A + 10B + C) - (100C + 10B + A) = 396
Simplifying this equation, we get:
99A - 99C = 396
Step 3: Let's further simplify the equation by canceling out the common factor of 99:
A - C = 4
Step 4: Now we know that the difference between the hundreds digit A and the units digit C is 4. We are also given that the difference between the hundreds and units digit is one less than the sum of the units and tens digit:
A - C = (B + C) - 1
Rearranging the equation, we get:
A + C = B + 1
Step 5: Now we have two equations:
A - C = 4
A + C = B + 1
Step 6: We can solve these equations simultaneously by adding them:
(A - C) + (A + C) = 4 + (B + 1)
This simplifies to:
2A = B + 5
Step 7: Based on the information provided, we are looking for a three-digit number. Therefore, A cannot be 0, and the lowest possible value for A is 1. Let's start with A = 1 and try different values for B and C to see if we find a valid solution.
If A = 1, then our equation becomes:
2(1) = B + 5
2 = B + 5
B = -3
Since B cannot be negative, the values of A and B don't work.
Step 8: Let's try the next possible value for A, which is 2. If A = 2, our equation becomes:
2(2) = B + 5
4 = B + 5
B = -1
Again, B cannot be negative, so these values don't work either.
Step 9: Finally, let's try A = 3. If A = 3, our equation becomes:
2(3) = B + 5
6 = B + 5
B = 1
Great! This value for B works. So, if A = 3 and B = 1, we can substitute these values into our original equation:
A - C = 4
3 - C = 4
C = 3
Therefore, the number we are looking for is 313.