Question : The average of twelve numbers is 58. The average of the first five numbers is 56 and the average of the next four numbers is 60. The 10th number is 4 more than the 11th number and the 11th number is one less than the 12th number. What is the average of the 10th and 12th numbers?
Option 1: 58.5
Option 2: 59.5
Option 3: 59
Option 4: 58
Correct Answer: 59.5
Solution :
Given,
The average of 12 numbers = 58
⇒ Sum of 12 numbers = 12 × 58 = 696
Also,
Average of first 5 numbers = 56
⇒ Sum of first 5 numbers = 5 × 56 = 280
Average of next 4 numbers = 60
⇒ Sum of next 4 numbers = 4 × 60 = 240
⇒ Sum of 10
th
, 11
th
and 12
th
numbers = 696 – 280 – 240 = 176
Let 12
th
number be
⇒ 11
th
number =
⇒ 10
th
number =
According to the question,
⇒
⇒
⇒
⇒ 12
th
number = 58
⇒ 10
th
number = 58 + 3 = 61
The average of 10
th
and 12
th
number =
Hence, the correct answer is 59.5.
