The total number of integers between 400 and 600, each of which, either begins with 5 or ends with 5 but not both, is-

The Correct answer is Option 2. 

Key Points

When 5 lies at hundred‟s place-

500, 501, 502, ..........., 599

Total number of integers = {(599 - 500)/1} + 1 = 100 ...(i)

[∵n = {(last number – first number)/common difference} + 1]

When 5 lies at unit‟s place-

405, 415, 425, 435, 445, 455, 465, 475, 485 and 495.

Total number of such integers = 10 .....(ii)

When 5 lies at both unit‟s and hundred‟s place-

505, 515, 525, 535, 545, 555, 565, 575, 585 and 595.

Total number of such integers = 10 ....(iii)

But these numbers are already included in equation (i). Hence, total number of integers between 400 and

600, each of which either begin with 5 or ends with 5 but not both = 100 + 10 – 10 = 100

Hence Option 2 is Correct.