Question

The difference between the greatest and the smallest 4-digit number that can be formed by the digits 5, 3, 0 and 8 such that 5 is always at the ones place and no digits are repeated is____
A. $$5085$$
B. $$5220$$
C. $$4950$$
D. $$4945$$

Answer 1

Hint: First we need to find the greatest and smallest 4-digit number that can be formed using the digits 5, 3, 0 and 8 such that in unit place 5 will be fixed. Taking the difference of these two we get the required answer. One place or unit place both are the same. We know that four digits will have units, tens, hundreds and thousands places.

Complete step-by-step answer:
We know that the four digit is $$\text{\_ \_ \_ \_}$$ .
To understand places of 4 digit place: see the figure

Since in the given question given that 5 is always in first place then we have, $$\underset{―}{}\underset{―}{}\underset{―}{}\underset{―}{5}$$ .
Now to fill the remaining places, we know that in order to make the greatest number from a given number, arrange the digit in descending order.
We have 5, 3, 0 and 8 arranging in descending form: $$8,5,3,0.$$
Also given that no two numbers are repeated, we have 5 already fixed in unit place so removing 5 we have $$8,3,0.$$
So, the greatest 4-digit number is $$8305$$ .
To find the smallest number arrange in ascending form we start digit other than 0 and write the 0 in hundredth place: $$3,0,8$$
So the smallest 4-digit number is $$3085$$ .
Hence the difference between them is $$=8305-3085$$
 $$=5220$$
So, the correct answer is “Option B”.

Note: Careful when 0 comes in first, if we write 0 in the thousand place it will become a three digit number, hence write 0 in the hundredth place. In case two digits are equal, we write them at consecutive places. Follow the same procedure for three and two digit numbers. Don’t get confused with the unit and one place both are the same.