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Set A contains 10 consecutive numbers starting from x and set B contains 8 consecutive even numbers starting from y. The ratio of the average of set A elements to that of set B elements is 9 : 14. What is the ratio of x to y?
- a)9 : 14
- b)14 : 9
- c)5 : 4
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Set A contains 10 consecutive numbers starting from x and set B contai...
Average of set A elements = x + 4.5
Average of set B elements = y + 7
So,
= 9/14
⇒ 14x + 63 = 9y + 63
⇒ x/y = 9/14
Average of set B elements = y + 7
So,
= 9/14⇒ 14x + 63 = 9y + 63
⇒ x/y = 9/14
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Community Answer
Set A contains 10 consecutive numbers starting from x and set B contai...
Let's assume that the first number in set A is x and the first number in set B is y.
Finding the average of set A:
Since set A contains 10 consecutive numbers starting from x, the sum of the numbers in set A can be found using the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)
In this case, the sum of the numbers in set A is (10/2) * (x + (x+9)) = 5 * (2x + 9) = 10x + 45.
The average of set A can be found by dividing the sum by the number of terms:
Average of set A = (10x + 45) / 10 = x + 4.5.
Finding the average of set B:
Since set B contains 8 consecutive even numbers starting from y, the sum of the numbers in set B can be found using the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)
In this case, the sum of the numbers in set B is (8/2) * (y + (y+14)) = 4 * (2y + 14) = 8y + 56.
The average of set B can be found by dividing the sum by the number of terms:
Average of set B = (8y + 56) / 8 = y + 7.
Ratio of the averages:
Given that the ratio of the average of set A elements to that of set B elements is 9:14, we can write the equation:
(x + 4.5) / (y + 7) = 9/14.
Cross-multiplying and simplifying the equation:
14(x + 4.5) = 9(y + 7)
14x + 63 = 9y + 63
14x = 9y
x/y = 9/14
Therefore, the ratio of x to y is 9:14. Hence, the correct answer is option A.
Finding the average of set A:
Since set A contains 10 consecutive numbers starting from x, the sum of the numbers in set A can be found using the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)
In this case, the sum of the numbers in set A is (10/2) * (x + (x+9)) = 5 * (2x + 9) = 10x + 45.
The average of set A can be found by dividing the sum by the number of terms:
Average of set A = (10x + 45) / 10 = x + 4.5.
Finding the average of set B:
Since set B contains 8 consecutive even numbers starting from y, the sum of the numbers in set B can be found using the formula for the sum of an arithmetic series:
Sum = (Number of terms / 2) * (First term + Last term)
In this case, the sum of the numbers in set B is (8/2) * (y + (y+14)) = 4 * (2y + 14) = 8y + 56.
The average of set B can be found by dividing the sum by the number of terms:
Average of set B = (8y + 56) / 8 = y + 7.
Ratio of the averages:
Given that the ratio of the average of set A elements to that of set B elements is 9:14, we can write the equation:
(x + 4.5) / (y + 7) = 9/14.
Cross-multiplying and simplifying the equation:
14(x + 4.5) = 9(y + 7)
14x + 63 = 9y + 63
14x = 9y
x/y = 9/14
Therefore, the ratio of x to y is 9:14. Hence, the correct answer is option A.
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Set A contains 10 consecutive numbers starting from x and set B contains 8 consecutive even numbers starting from y. The ratio of the average of set A elements to that of set B elements is 9 : 14. What is the ratio of x to y?a)9 : 14b)14 : 9c)5 : 4d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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