Question:
The average of 9 consecutive odd numbers is 53. If the next 4 consecutive odd numbers are also included, what will be the new average?
9 क्रमागत विषम संख्याओं का औसत 53 है। यदि अगली 4 क्रमागत विषम संख्याओं को भी शामिल कर लिया जाए, तो नया औसत क्या होगा?
Options:
- 57
- 55
- 59
- 61
- 57
- 55
- 59
- 61
Correct Answer: a)
Explanation:
For any set of consecutive odd numbers, when \(k\) next consecutive odd numbers are added, the average increases by \(k\).
Here, \(k = 4\).
Therefore, New Average = \(53 + 4 = 57\).
Proof: The middle number of 9 consecutive odd numbers is 53 (5th number).
Numbers are: 45, 47, 49, 51, 53, 55, 57, 59, 61.
Next 4 odd numbers are: 63, 65, 67, 69.
Total 13 numbers. Middle number is the 7th number, which is 57.
Here, \(k = 4\).
Therefore, New Average = \(53 + 4 = 57\).
Proof: The middle number of 9 consecutive odd numbers is 53 (5th number).
Numbers are: 45, 47, 49, 51, 53, 55, 57, 59, 61.
Next 4 odd numbers are: 63, 65, 67, 69.
Total 13 numbers. Middle number is the 7th number, which is 57.
क्रमागत विषम संख्याओं के गुणधर्म के अनुसार, जब अगली \(k\) क्रमागत विषम संख्याएं जोड़ी जाती हैं, तो औसत \(k\) बढ़ जाता है।
यहाँ \(k = 4\), अतः नया औसत = \(53 + 4 = 57\)।
यहाँ \(k = 4\), अतः नया औसत = \(53 + 4 = 57\)।