Of the 5 subjects, the average marks of Rakesh in first 3 subjects was 80 and the average marks in the last 3 subjects was 92. If his marks in the third subject was 51, then what was his average marks in all the 5 subjects?

Correct option is D

​Given:
- Average marks in the first 3 subjects = 80
- Average marks in the last 3 subjects = 92
- Marks in the third subject = 51

Formula Used:

Total Marks = $$\text{Average} \times \text{Number of Subjects}$$

$$\text{Average of all subjects} = \frac{\text{Total Marks}}{\text{Number of Subjects}}$$​​
Solution:
Let the marks in the first three subjects be  $$M_1, M_2, M_3$$​and the marks in the last three subjects be $$M_3, M_4, M_5$$​ where $$M_3 = 51$$​
Total marks in the first 3 subjects:

$$M_1 + M_2 + M_3 = 80 \times 3 = 240$$​​
Thus, $$M_1 + M_2 + 51 = 240$$​ which gives:

$$M_1 + M_2 = 240 - 51 = 189$$​​
Total marks in the last 3 subjects:

$$M_3 + M_4 + M_5 = 92 \times 3 = 276$$​​
Thus,$$51 + M_4 + M_5 = 276$$​ , which gives:

$$M_4 + M_5 = 276 - 51 = 225$$​​
Total marks in all 5 subjects:

$$M_1 + M_2 + M_3 + M_4 + M_5 = 189 + 51 + 225 = 465\\\ \\Average = \frac{465}{5} = 93$$​​
The average marks in all 5 subjects is 93 .

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