The average of thirteen numbers is 47. The average of the first three numbers is 39 and that of next seven numbers is 49. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of 11th and 13th numbers?
Answers
I think it's a 57 by calculation
Solution:
Let 12th number be m.
According to question,
11th number would be 2m
13th number would be (m+3)
Average = Total of given numbers / Count of given numbers
Total of given numbers = Average x Count of given numbers
Average of first three numbers is 39 .
So , Total of first three numbers would be = 39 x 3 = 117
Average of next seven numbers is 49.
So, Total of next seven numbers (i.e. 4th to 10th numbers) = 49 x 7 = 343
Total from 11th to 13th numbers = 2m + m + (m + 3)
Average of all thirteen numbers is 47.
Total of numbers from 1st to 13th = 47 x 13 = 611
Now,
Total of first three numbers + Total of 4th to 10th numbers + Total of 11th to 13th Numbers = Total of all thirteen numbers
117 + 343 + 2m + m + m + 3 = 611
463 + 4m = 611
4m = 611 - 463
m = 148 / 4
m = 37
11th number = 2m = 2 x 37 = 74
12th number = m = 37
13th number = m + 3 = 37 + 3 = 40
Average of 11th and 13th number = (74 + 40) / 2 = 114 / 2 = 57
Average of 11th and 13th number is 57.