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 $x$
⇒ 11
th
number = $x - 1$
⇒ 10
th
number = $x + 3$
According to the question,
$x + x – 1 + x + 3 = 176$
⇒ $3x = 176 -2 $
⇒ $x = \frac{174}{3}$
⇒ $x = 58$
⇒ 12
th
number = 58
⇒ 10
th
number = 58 + 3 = 61
The average of 10
th
and 12
th
number = $\frac{58 + 61}{2}$ = 59.5
Hence, the correct answer is 59.5.
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