The average of thirteen numbers is 57. The average of first three numbers is 48, and that of the next seven numbers is 58. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of the 11th and 13th numbers?

Correct option is B

Given:
Average of 13 numbers = 57
Average of 1st three numbers = 48
Average of next 7 numbers (4th to 10th) = 58
Solution:
Average of 13 numbers = 57
=> Total sum of 13 numbers = 13 × 57 = 741
Average of 1st three numbers = 48
=> Sum of 1st three numbers = 3 × 48 = 144
Average of next 7 numbers (4th to 10th) = 58
=> Sum of 4th to 10th numbers = 7 × 58 = 406
Let the 13th number be x
=> 12th number = x – 3
=> 11th number = 2(x – 3) = 2x – 6
Total sum = Sum of (1st 3 numbers) + (4th to 10th numbers) + 11th + 12th + 13th
=> 741 = 144 + 406 + (2x – 6) + (x – 3) + x
741 = 144 + 406 + (2x – 6) + (x – 3) + x
= 741 = 550 + 4x – 9
= 741 = 541 + 4x
=> 4x = 200
=> x = 50
13th number = x = 50
12th number = x – 3 = 47
11th number = 2 × 47 = 94
Average of 11th and 13th numbers =$$\frac{94 + 50} 2$$​ = 72