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The mean weight of a group of 10 items is 28 and that of another group of n items is 35. The mean of combined group of 10 + n items is found to be 30. The value of n is
- a)2
- b)4
- c)10
- d)12
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The mean weight of a group of 10 items is 28 and that of another group...
Given:
- Mean weight of a group of 10 items = 28
- Mean weight of another group of n items = 35
- Mean weight of combined group of 10 + n items = 30
To Find:
The value of n
Solution:
Let's first calculate the total weight of the first group of 10 items.
Total weight of the first group = Mean weight × Number of items
Total weight of the first group = 28 × 10
Total weight of the first group = 280
Similarly, let's calculate the total weight of the second group of n items.
Total weight of the second group = Mean weight × Number of items
Total weight of the second group = 35 × n
Total weight of the second group = 35n
Now, let's consider the combined group of 10 + n items.
Total weight of the combined group = Mean weight × Number of items
Total weight of the combined group = 30 × (10 + n)
Total weight of the combined group = 300 + 30n
Since the total weight of the combined group is the sum of the total weights of the first and second groups, we can write the equation:
Total weight of the combined group = Total weight of the first group + Total weight of the second group
300 + 30n = 280 + 35n
Simplifying the equation, we get:
300 - 280 = 35n - 30n
20 = 5n
n = 20/5
n = 4
Therefore, the value of n is 4.
Hence, the correct option is (b) 4.
- Mean weight of a group of 10 items = 28
- Mean weight of another group of n items = 35
- Mean weight of combined group of 10 + n items = 30
To Find:
The value of n
Solution:
Let's first calculate the total weight of the first group of 10 items.
Total weight of the first group = Mean weight × Number of items
Total weight of the first group = 28 × 10
Total weight of the first group = 280
Similarly, let's calculate the total weight of the second group of n items.
Total weight of the second group = Mean weight × Number of items
Total weight of the second group = 35 × n
Total weight of the second group = 35n
Now, let's consider the combined group of 10 + n items.
Total weight of the combined group = Mean weight × Number of items
Total weight of the combined group = 30 × (10 + n)
Total weight of the combined group = 300 + 30n
Since the total weight of the combined group is the sum of the total weights of the first and second groups, we can write the equation:
Total weight of the combined group = Total weight of the first group + Total weight of the second group
300 + 30n = 280 + 35n
Simplifying the equation, we get:
300 - 280 = 35n - 30n
20 = 5n
n = 20/5
n = 4
Therefore, the value of n is 4.
Hence, the correct option is (b) 4.
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The mean weight of a group of 10 items is 28 and that of another group of n items is 35. The mean of combined group of 10 + n items is found to be 30. The value of n isa)2b)4c)10d)12Correct answer is option 'B'. Can you explain this answer?
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