How many numbers lie between 300 and 500 in which 4 comes only one time?

To find the numbers between 300 and 500 where 4 appears exactly once, we split the range into two parts.

First, consider the range from 300 to 399. In these 100 numbers, the hundreds digit is 3. We need 4 to appear once in the tens or units place. If 4 is in the tens place, it looks like 34X. X can be any digit from 0 to 9 except 4, giving us 9 options. If 4 is in the units place, it looks like 3X4. X can be any digit from 0 to 9 except 4, giving us 9 options. Total for this range is 9 plus 9 which equals 18.

Second, consider the range from 400 to 499. In these 100 numbers, the digit 4 is already fixed in the hundreds place. For 4 to appear only once, it must not appear in the tens or units place. The tens place has 9 options (0 to 9 excluding 4) and the units place has 9 options (0 to 9 excluding 4). Total for this range is 9 times 9 which equals 81.

Finally, we add the two parts together. 18 plus 81 equals 99. The number 500 does not contain 4, so it does not change the count. Therefore, there are 99 such numbers.