The number of natural numbers belonging to `(20000, 60000]`, whose sum of digits is even, is

Options

A. 40000
B. 20000
C. 5000
D. 25000

Explanation

The number lying between 20,000 and 60,000 will be five digit number having 2,3,4 or 5 at ten thousands place. So, the ten thousands place can be filled in 4 ways.

Each of thousands, hundreds and tens places can be filled in 10 ways. So, the first four places can be filled in
`4xx10xx10xx10` ways.
After filling these the sum of the digits at these four places is either even or odd. Therefore, the units place can be filled by one of the digits 0, 2, 4, 6, 8 when the sum is even and if the sum is odd, the units place can be filled by one of the digits 1, 3, 5, 7, 9. In either case, the units place is filled in 5 ways. Hence, the required number of numbers
`=4xx10xx10xx10xx5=20,000`.