10 digit numbers are formed using all the digit 0 to 9 such that are divisible by 11111. The digit in 10th place of smallest of such number and  digit at unit position of such number.

Arun
25750 Points
5 years ago
This question can be answered by using our common sense.

We know that
11111 × 90000 = 999990000
By intuition, we can conclude that 10000 is the smallest number which when added to
999990000 will give a 10 digited sum.
As 11111 > 10000,
11111*90001 will be the smallest 10 digit number satisfying a given condition.
Needless to tell,
its 10's digit = 1.

By using a bit common sense, we can predict that the largest 10 digit multiple of 11111 should be 9999999999.
Unit digit = 9.

Again let's use a bit common sense instead of using horrible A. P. formulae.
Before directly jumping to our problem, I'd love to give some introduction.
Suppose we've to find the multiples of 5 between 28 & 52.
What shall we do ?
The smallest multiple = 30.
The greatest multiple = 50.
30/5 = 6 & 50/5 = 10.
Total number of multiples =
(10-6) + 1 = 5.
Now, let's turn towards our problem.
Now, I think the next steps are very clear.
We have :
11111*90001/11111 = 90,001.
9999999999/11111 = 9,00,009.
Number of 10 digit multiples of 11111 = 9,00,009 - 90,001 + 1
= 9,00,009 - 90,000
= 8,10,009.