Question : The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth numbers is:
Option 1: 47
Option 2: 39
Option 3: 44
Option 4: 50
Correct Answer: 47
Solution :
The average of twelve numbers is 39.
Sum of twelve numbers = 39 × 12 = 468
The average of the last five numbers = 35
The sum of last five numbers = 35 × 5 = 175
Average of the first four numbers = 40
The sum of the first four numbers = 40 × 4 = 160
Let $x$ be the fifth number.
Sixth number = $x+6$
Seventh number = $x-5$
So, $160 + x + x+6 + x-5 + 175 = 468$
⇒ $3x = 468-336$
⇒ $x = \frac{132}{3} = 44$
Average of fifth and sixth number = $\frac{44+50}{2}$ = 47
Hence, the correct answer is 47.
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