'abc' is a number. Where a, b, c each of them is a single digit. If (a - c) = 5 then, what's the value of (abc - cba)??
Solve it with explanation.
All the best :D
Answers
Answer:
ABC - CBA = 495
Step-by-step explanation:
We can solve it in two ways,
Method 1 (Simple Substitution)
We have,
ABC where A, B, and C are digits.
(A - C) = 5
Then,
ABC = 100A + 10B + C
Also,
CBA = 100C + 10B + A
We need,
ABC - CBA = (100A + 10B + C) - (100C + 10B + A)
= 100A + 10B + C - 100C - 10B - A
= 100A - A + 10B - 10B + C - 100C
= 99A - 99C
(Taking Common factor 99)
= 99(A - C)
Now,
We have,
(A - C) = 5
Then,
ABC - CBA = 99(5)
ABC - CBA = 495
Hence,
ABC - CBA = 495
Method 2 (Logic and Reasoning)
In this method, we will be looking deeper into simple subtraction and how something like subtraction could be so interesting!!!
We have,
ABC is a 3 digit number,
(A - C) = 5
Since,
A - C = 5
we can say that,
A > C because only if A is greater than C will we get a positive number which is 5,
For ex:-
4 - 2 = 2
Here,
4 > 2, as it gave a positive answer
Again,
2 - 4 = (-2)
Here,
2 < 4 as it gave a negative answer.
So,
we conclude that A > C
Now, let's start with the subtraction,
ABC
- CBA
————
————
So,
First we must subtract C - A,
But we know that,
A > C,
So,
C - A will give a negative answer, but in simple subtraction, that is not possible, so we borrow 10 from B of ABC.
If you notice in Subtraction, borrowing is always in 10.
For ex:-
²3¹3
- 9
———
24
———
Now,
If you notice the above calculation, 3 - 9 is not possible in simple subtraction, so there will be borrowing, here the 3 became 13 so, the subtraction changed to 13 - 9 = 4
Similarly,
In our problem also we can use the same property,
Since,
C < A
We borrow from B, but then B becomes (B - 1)
[Its the B from ABC, not CBA]
So,
(10 + C) - A
= 10 + C - A
= 10 + (C - A)
If we take the common factor as (-1),
= 10 + (-1)(A - C)
Now,
A - C = 5,
= 10 + (-1)(5)
= 10 + (-5)
= 10 - 5
= 5
So,
ABC
- CBA
———
5
———
Next, we must find,
(B - 1) - B
Again,
We can see clearly that,
(B - 1) < B
So,
Borrowing is required again, now we borrow from A,
So,
After borrow (B - 1) will become (10 + B - 1) and A will become (A - 1)
Now,
(10 + B - 1) - B
= 10 - 1 + B - B
= 9
Thus,
ABC
- CBA
———
95
———
Next, we must find,
(A - 1) - C
Now, if we rearrange,
= (A - 1) - C
= A - 1 - C
= A - C - 1
= (A - C) - 1
Now,
we know that,
A - C = 5
So,
= (5) - 1
= 4
Thus,
ABC
- CBA
———
495
———
Hence,
ABC - CBA = 495
Hope it helped and believing you understood it........All the best
ABC - CBA = 495
is the answer for your question