The average of six numbers is 48. If the average of first four is 28 and that of last three is 41, the fourth number is: Options :475149none of these

Sure, let's solve this step by step:

1. The average of six numbers is 48. This means the total sum of these six numbers is 48 * 6 = 288.

2. The average of the first four numbers is 28. This means the total sum of these four numbers is 28 * 4 = 112.

3. The average of the last three numbers is 41. This means the total sum of these three numbers is 41 * 3 = 123.

4. Now, the fourth number is included in both the first four numbers and the last three numbers. So, to find the fourth number, we subtract the sum of the first three numbers and the sum of the last two numbers from the total sum of all six numbers.

5. The sum of the first three numbers is 112 (sum of first four numbers) - x (fourth number). The sum of the last two numbers is 123 (sum of last three numbers) - x (fourth number).

6. Therefore, the fourth number x = (total sum of all six numbers) - (sum of first three numbers + sum of last two numbers) = 288 - (112 + 123 - 2x).

7. Solving this equation for x gives x = 53.

So, the fourth number is 53.