50000

Sol. We have to count the occurrences of digit 5 consider integers t such that 0 ≤ t ≤ 10 5

The largest number t having 5 in the units place is 99995.So there are

1 + 9999 = 10 4 numbers t having 5 in the units place

The are 5, 15, 25,............99995

We can describe these numbers as t = x 5

Where x is any one of 0, 1, 2,......9999. Similarly numbers t = x5y.

ie.e., numbers having 5 in the ten's place are in all (1 + 999) × 10 = 10 4 as x can be any one of 0, 1, 2,..999 and y can be anyone of 0, 1,2,.......9

In the same way, there are 10 4 numbers in each of the following cases: numbers with 5 in the hundreds place or thousands place or ten thousands place.

Hence, the total number of times 5 is written 10 4 × 5

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