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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.

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.

Grade:12th pass

1 Answers

Arun
25763 Points
2 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.

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