College P has 180 students scoring average marks of 88 and college Q has 320 students scoring average marks of 72. Find the average marks of both the colleges together.

College P: 180 students with an average of 88 marks.

College Q: 320 students with an average of 72 marks.

​$$\text{Combined Average} = \frac{\text{Total Marks of P} + \text{Total Marks of Q}}{\text{Total Students of P and Q}}.$$​​

​$$\text{Total Marks of P} = 180 \times 88 = 15,840.\\\text{Total Marks of Q} = 320 \times 72 = 23,040 \\\text{Total Marks} = 15,840 + 23,040 = 38,880.\\\text{Total Students} = 180 + 320 = 500. \\\text{Combined Average} = \frac{38,880}{500} = 77.76$$​​

$$\therefore$$​ The average marks of both colleges together is 77.76.

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