The average of thirteen numbers is 47. The average of first 3 numbers is 39 and that of next 7 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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 ie 57.
= (sum of 13 numbers) / 13 = 47
Avg. of first 3 numbers = 39
Avg. of next 7 numbers = 49
Let the 12th number be x.
Then, 11th number = 2x.
13th number = x+3
Now,
(39 × 3) + (49 × 7) + 3x + (x + 3) = 47 × 13
4x + 120 + 343 = 47 × 13
4x = 148
x = 37
Avg. of 11th and 13th number = (2x + x + 3) / 2
= [3(37) + 1] / 2
= 57