The average of twelve numbers is 42. The average of the last five numbers is 40, and that of the first four numbers is 44. The sixth number is 6 less than the fifth number and 5 less than the seventh number. The average of the sixth and seventh numbers is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 41.5.
We know that,
Average = Sum of observations/Number of observations
Now,
Sum of 12 numbers = 12 × 42 = 504
Sum of first four numbers = 44 × 4 = 176
Sum of last five numbers = 40 × 5 = 200
Let the 6th number be a
7th number = a + 5
5th number = a + 6
Sum of 5th, 6th and 7th numbers = 504 - 176 - 200 = 128
Thus, a + 6 + a + a + 5 = 128
⇒ 3a + 11 = 128
⇒ 3a = 117
⇒ a = 39
6th and 7th numbers will be 39 and 44
Average of 6th and 7th numbers = (39 + 44)/2 = 41.5