व्हाट इज द जनरल फॉर्म ऑफ 3 डिजिट नंबर
Answers
In general, a 3-digit number abc made up of digits a, b and c is written as
abc = 100 × a + 10 × b + 1 × c
= 100a + 10b + c
In the same way,
cab = 100c + 10a + b
bca = 100b + 10c + a and so on.
Answer:
Numbers in General Form
Let us take the number 52 and write it as
52 = 50 + 2 = 10 × 5 + 2
Similarly, the number 37 can be written as
37 = 10 × 3 + 7
In general, any two digit number ab made of digits a and b can be written as
ab = 10 × a + b = 10a + b
ba = 10 × b + a = 10b + a
Let us now take number 351. This is a three digit number. It can also be written as
351 = 300 + 50 + 1 = 100 × 3 + 10 × 5 + 1 × 1
497 = 100 × 4 + 10 × 9 + 1 × 7
Similarly, In general, a 3-digit number abc made up of digits a, b and c is written as
abc = 100 × a + 10 × b + 1 × c
= 100a + 10b + c
In the same way,
cab = 100c + 10a + b
bca = 100b + 10c + a and so on.
Solution: This also has two letters A and B whose values are to be found. Since the ones digit of 3 × A is A, it must be that A = 0 or A = 5.
Now look at B. If B = 1, then BA × B3 would at most be equal to 19 × 19; that is, it would at most be equal to 361. But the product here is 57A, which is more than 500. So we cannot have B = 1.
If B = 3, then BA × B3 would be more than 30 × 30; that is, more than 900. But 57A is less than 600. So, B can not be equal to 3. Putting these two facts together, we see that B = 2 only. So the multiplication is either 20 × 23, or 25 × 23. The first possibility fails, since 20 × 23 = 460. But, the second one works out correctly, since 25 × 23 = 575. So the answer is A = 5, B = 2.
Summary
Numbers can be written in general form. Thus, a two digit number ab will be written as ab = 10a + b.
The sum of a 2-digit number and the number obtained by interchanging its digits is always divisible by 11.
The difference between a 2-digit number and the number obtained by interchanging its digits is always divisible by 9.
The general form of a 3-digit number is 100a +10b + c.
The difference between a 3-digit number and a number obtained by reversing its digits is always divisible by 99.
The general form of numbers are helpful in solving puzzles or number games.
Explanation:
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