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Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.
Find the average weight of all the students.
Correct answer is '54'. Can you explain this answer?
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Verified Answer
Five students went to a doctor for regular checkup. Doctor asked his a...
Let p, q, r, s, t be the weight of 5 students. Let us assume that p < q < r < s < t.
From the information mentioned above.
The three lightest students will have the least weight.
Hence, p + q + r = 95 (i)
The two lightest students and the fourth lightest student will have the second least weight.
p + q + s = 120 (ii)
The three heaviest students will have the highest weight.
r + s + t = 225 (iii)
The two heaviest students and the fourth heaviest student will have the second highest weight.
q + s + t = 200 (iv)
Since the students are weighed in triplets, 10 weightings mean each student is weighed 6 times.
Hence, 6(p + q + r + s + t) = 95 + 150 + 145 + 120 + 145 + 175 + 170 + 200 + 195 + 225 = 1620
=> p + q + r + s + t = 270 (v)
(i) + (iii) - (v) => r = 50
(i) + (iv) - (v) => q = 25
(ii) + (iii) - (v) => s = 75
Putting the values of q and r in (i), we get p=20
Putting the values of r and s in (iii), we get t=100
Average weight of all the students = (p + q + r + s + t)/5 = (20 + 25 + 50 + 75 +100)/5 = 270/5 = 54kg.
From the information mentioned above.
The three lightest students will have the least weight.
Hence, p + q + r = 95 (i)
The two lightest students and the fourth lightest student will have the second least weight.
p + q + s = 120 (ii)
The three heaviest students will have the highest weight.
r + s + t = 225 (iii)
The two heaviest students and the fourth heaviest student will have the second highest weight.
q + s + t = 200 (iv)
Since the students are weighed in triplets, 10 weightings mean each student is weighed 6 times.
Hence, 6(p + q + r + s + t) = 95 + 150 + 145 + 120 + 145 + 175 + 170 + 200 + 195 + 225 = 1620
=> p + q + r + s + t = 270 (v)
(i) + (iii) - (v) => r = 50
(i) + (iv) - (v) => q = 25
(ii) + (iii) - (v) => s = 75
Putting the values of q and r in (i), we get p=20
Putting the values of r and s in (iii), we get t=100
Average weight of all the students = (p + q + r + s + t)/5 = (20 + 25 + 50 + 75 +100)/5 = 270/5 = 54kg.
Most Upvoted Answer
Five students went to a doctor for regular checkup. Doctor asked his a...
Let's call the weights of the five students A, B, C, D, and E. We need to find the weights of each student using the given measurements.
First, we notice that the weights are given in pairs: (95kg, 150kg), (125kg, 120kg), (145kg, 175kg), and (170kg, 200kg). This suggests that each pair is made up of the weights of two different students.
Let's consider the pair (95kg, 150kg). We know that the weights of the students must be more than 80kg. Therefore, the weight of the lighter student in this pair must be 95kg. This means that the heavier student must weigh 150kg.
Next, let's consider the pair (125kg, 120kg). Again, the weight of the lighter student must be 120kg, and the weight of the heavier student must be 125kg.
Moving on to the pair (145kg, 175kg), we can determine that the weight of the lighter student is 145kg and the weight of the heavier student is 175kg.
Finally, we have the pair (170kg, 200kg). The weight of the lighter student is 170kg, and the weight of the heavier student is 200kg.
Now we have the weights of four students: A = 95kg, B = 150kg, C = 120kg, and D = 125kg. To find the weight of the fifth student, E, we can subtract the weights of these four students from the total weight obtained from the measurements. The total weight is 195kg (from 95kg + 150kg), so E = 195kg - (A + B + C + D).
E = 195kg - (95kg + 150kg + 120kg + 125kg) = 195kg - 490kg = -295kg
Since the weight cannot be negative, it is not possible to determine the weight of the fifth student using the given measurements.
First, we notice that the weights are given in pairs: (95kg, 150kg), (125kg, 120kg), (145kg, 175kg), and (170kg, 200kg). This suggests that each pair is made up of the weights of two different students.
Let's consider the pair (95kg, 150kg). We know that the weights of the students must be more than 80kg. Therefore, the weight of the lighter student in this pair must be 95kg. This means that the heavier student must weigh 150kg.
Next, let's consider the pair (125kg, 120kg). Again, the weight of the lighter student must be 120kg, and the weight of the heavier student must be 125kg.
Moving on to the pair (145kg, 175kg), we can determine that the weight of the lighter student is 145kg and the weight of the heavier student is 175kg.
Finally, we have the pair (170kg, 200kg). The weight of the lighter student is 170kg, and the weight of the heavier student is 200kg.
Now we have the weights of four students: A = 95kg, B = 150kg, C = 120kg, and D = 125kg. To find the weight of the fifth student, E, we can subtract the weights of these four students from the total weight obtained from the measurements. The total weight is 195kg (from 95kg + 150kg), so E = 195kg - (A + B + C + D).
E = 195kg - (95kg + 150kg + 120kg + 125kg) = 195kg - 490kg = -295kg
Since the weight cannot be negative, it is not possible to determine the weight of the fifth student using the given measurements.
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Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer?
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Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer?.
Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer?.
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Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer?, a detailed solution for Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? has been provided alongside types of Five students went to a doctor for regular checkup. Doctor asked his assistant to measure the weight of these students. But the problem is that the weighing machine that assistant has measures only those weights which are more than 80kg. So assistant thought to measure weight of 3 students at a time and he weighed all the possible combinations of weight of students. He obtained the measurements as 95kg, 150kg, 125kg, 120kg, 145kg, 175kg, 170kg, 200kg, 195kg & 225kg.Find the average weight of all the students.Correct answer is '54'. Can you explain this answer? theory, EduRev gives you an
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