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Suppose the average weight of9 persons is 50 kg. The average weight of the first5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the5th person will be
- a)45 kg
- b)47.5 kg
- c)50 kg
- d)52.5 Kg
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Suppose the average weight of9 persons is 50 kg. The average weight of...
Weight of fifth person = (5 × 45 + 5 × 55) – 9 × 50
= (225 + 275) – 450
= 500 – 450 = 50 kg
= (225 + 275) – 450
= 500 – 450 = 50 kg
Most Upvoted Answer
Suppose the average weight of9 persons is 50 kg. The average weight of...
Given Information:
- The average weight of 9 persons is 50 kg.
- The average weight of the first 5 persons is 45 kg.
- The average weight of the last 5 persons is 55 kg.
To find: The weight of the 5th person.
Solution:
Let's assume the weight of the 9 persons are as follows -
- w1, w2, w3, w4, w5, w6, w7, w8, w9
Now, we can use the formula for the average weight of n persons, which is:
Average weight of n persons = (Sum of weights of all persons) / n
Using this formula, we can write the following equations -
- (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9) / 9 = 50 (Average weight of 9 persons is 50 kg)
- (w1 + w2 + w3 + w4 + w5) / 5 = 45 (Average weight of the first 5 persons is 45 kg)
- (w5 + w6 + w7 + w8 + w9) / 5 = 55 (Average weight of the last 5 persons is 55 kg)
We can simplify these equations as follows -
- w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 = 450 (Multiplying both sides by 9)
- w1 + w2 + w3 + w4 + w5 = 225 (Multiplying both sides by 5)
- w5 + w6 + w7 + w8 + w9 = 275 (Multiplying both sides by 5)
Subtracting equation 2 from equation 1, we get -
- w6 + w7 + w8 + w9 = 225 (Subtracting both sides by w1 + w2 + w3 + w4 + w5)
Subtracting equation 3 from equation 1, we get -
- w1 + w2 + w3 + w4 = 175 (Subtracting both sides by w5 + w6 + w7 + w8 + w9)
Now, we need to find the weight of the 5th person, which is w5.
Adding equations 2 and 3, we get -
- w5 + w6 + w7 + w8 + w9 + w1 + w2 + w3 + w4 = 500 (Adding both sides)
Substituting the values we have found earlier, we get -
- w5 + 275 + 225 = 500 (Substituting w5 + w6 + w7 + w8 + w9 = 275 and w1 + w2 + w3 + w4 = 175)
Simplifying, we get -
- w5 = 50
Therefore, the weight of the 5th person is 50 kg, which is option C.
- The average weight of 9 persons is 50 kg.
- The average weight of the first 5 persons is 45 kg.
- The average weight of the last 5 persons is 55 kg.
To find: The weight of the 5th person.
Solution:
Let's assume the weight of the 9 persons are as follows -
- w1, w2, w3, w4, w5, w6, w7, w8, w9
Now, we can use the formula for the average weight of n persons, which is:
Average weight of n persons = (Sum of weights of all persons) / n
Using this formula, we can write the following equations -
- (w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9) / 9 = 50 (Average weight of 9 persons is 50 kg)
- (w1 + w2 + w3 + w4 + w5) / 5 = 45 (Average weight of the first 5 persons is 45 kg)
- (w5 + w6 + w7 + w8 + w9) / 5 = 55 (Average weight of the last 5 persons is 55 kg)
We can simplify these equations as follows -
- w1 + w2 + w3 + w4 + w5 + w6 + w7 + w8 + w9 = 450 (Multiplying both sides by 9)
- w1 + w2 + w3 + w4 + w5 = 225 (Multiplying both sides by 5)
- w5 + w6 + w7 + w8 + w9 = 275 (Multiplying both sides by 5)
Subtracting equation 2 from equation 1, we get -
- w6 + w7 + w8 + w9 = 225 (Subtracting both sides by w1 + w2 + w3 + w4 + w5)
Subtracting equation 3 from equation 1, we get -
- w1 + w2 + w3 + w4 = 175 (Subtracting both sides by w5 + w6 + w7 + w8 + w9)
Now, we need to find the weight of the 5th person, which is w5.
Adding equations 2 and 3, we get -
- w5 + w6 + w7 + w8 + w9 + w1 + w2 + w3 + w4 = 500 (Adding both sides)
Substituting the values we have found earlier, we get -
- w5 + 275 + 225 = 500 (Substituting w5 + w6 + w7 + w8 + w9 = 275 and w1 + w2 + w3 + w4 = 175)
Simplifying, we get -
- w5 = 50
Therefore, the weight of the 5th person is 50 kg, which is option C.
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Suppose the average weight of9 persons is 50 kg. The average weight of the first5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the5th person will bea)45 kgb)47.5 kgc)50 kgd)52.5 KgCorrect answer is option 'C'. Can you explain this answer?
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Suppose the average weight of9 persons is 50 kg. The average weight of the first5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the5th person will bea)45 kgb)47.5 kgc)50 kgd)52.5 KgCorrect answer is option 'C'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Suppose the average weight of9 persons is 50 kg. The average weight of the first5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the5th person will bea)45 kgb)47.5 kgc)50 kgd)52.5 KgCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the average weight of9 persons is 50 kg. The average weight of the first5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg. Then the weight of the5th person will bea)45 kgb)47.5 kgc)50 kgd)52.5 KgCorrect answer is option 'C'. Can you explain this answer?.
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