Question : The average of 11 numbers is 36, whereas the average of 9 of them is 34. If the remaining two numbers are in the ratio of 2 : 3, find the value of the smaller number (between the remaining two numbers).
Option 1: 45
Option 2: 48
Option 3: 54
Option 4: 36
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Correct Answer: 36
Solution :
Given:
The average of 11 numbers is 36.
⇒ Total of 11 numbers = 36 × 11 = 396
The average of 9 of them is 34.
⇒ Total of 9 numbers = 34 × 9 = 306
$\therefore$ Total of the remaining two numbers = (396 – 306) = 90
The remaining two numbers are in the ratio of 2 : 3.
Therefore, the smaller number = $\frac{2}{2+3}×90$ = 36
Hence, the correct answer is 36.
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