The average of 15 numbers is 72. The average of the first 6 numbers is 65. The average of the next 5 numbers is 20% higher than the average of the first 6. The 12th number is 8 less than the 15th, and the 13th is 5 greater than the 15th and if 14th number is 78. What is the average of the 12th and 13th numbers?

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1. Compute sums: total = $15	imes72=1080$. First 6 sum = $6	imes65=390$. Next 5 avg = $65	imes1.2=78$, so sum = $5	imes78=390$.

2. Sum of last four = $1080-390-390=300$.

3. Let 15th be $x$. Then 12th $=x-8$, 13th $=x+5$, 14th $=78$. So $(x-8)+(x+5)+78+x=3x+75=300$. Thus $x=75$.

4. Average of 12th and 13th = $\dfrac{(x-8)+(x+5)}{2}=\dfrac{2x-3}{2}=x-1.5=75-1.5=73.5$.

FINAL_ANSWER: a

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