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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?
Most Upvoted Answer
Five students went to a doctor for regular checkup. Doctor asked his ...
To solve this problem, we need to find the weights of each individual student.
Let's assume the weights of the five students are A, B, C, D, and E.
From the given measurements, we can see that the sum of any three weights is greater than 240kg (80kg * 3).
Now, let's look at the combinations of three weights that can be calculated from the measurements:
A + B + C = 95kg
A + B + D = 150kg
A + B + E = 125kg
A + C + D = 120kg
A + C + E = 145kg
A + D + E = 175kg
B + C + D = 170kg
B + C + E = 200kg
B + D + E = 195kg
C + D + E = ? (unknown)
We can use these equations to find the weights of the individual students.
From the equation A + B + C = 95kg, we can substitute the values of A, B, and C from the other equations to get:
(150kg - D) + (125kg - E) + C = 95kg
275kg - D - E + C = 95kg
D + E - C = 180kg (Equation 1)
From the equation A + B + D = 150kg, we can substitute the values of A, B, and D from the other equations to get:
(125kg - E) + C + (175kg - E) = 150kg
300kg - 2E + C = 150kg
2E - C = 150kg (Equation 2)
Now, let's solve these two equations simultaneously:
2E - C = 150kg (Equation 2)
D + E - C = 180kg (Equation 1)
Adding Equation 1 and Equation 2, we get:
3E = 330kg
E = 110kg
Substituting the value of E into Equation 2, we get:
2(110kg) - C = 150kg
220kg - C = 150kg
C = 70kg
Substituting the values of E and C into Equation 1, we get:
D + 110kg - 70kg = 180kg
D = 140kg
Now, we can substitute the values of D, C, and E into the equation A + B + C = 95kg to find A and B:
A + B + 70kg = 95kg
A + B = 25kg
Since there are no additional equations involving A and B, we cannot determine their exact values.
Therefore, the weights of the five students are:
A + B = 25kg
C = 70kg
D = 140kg
E = 110kg
Let's assume the weights of the five students are A, B, C, D, and E.
From the given measurements, we can see that the sum of any three weights is greater than 240kg (80kg * 3).
Now, let's look at the combinations of three weights that can be calculated from the measurements:
A + B + C = 95kg
A + B + D = 150kg
A + B + E = 125kg
A + C + D = 120kg
A + C + E = 145kg
A + D + E = 175kg
B + C + D = 170kg
B + C + E = 200kg
B + D + E = 195kg
C + D + E = ? (unknown)
We can use these equations to find the weights of the individual students.
From the equation A + B + C = 95kg, we can substitute the values of A, B, and C from the other equations to get:
(150kg - D) + (125kg - E) + C = 95kg
275kg - D - E + C = 95kg
D + E - C = 180kg (Equation 1)
From the equation A + B + D = 150kg, we can substitute the values of A, B, and D from the other equations to get:
(125kg - E) + C + (175kg - E) = 150kg
300kg - 2E + C = 150kg
2E - C = 150kg (Equation 2)
Now, let's solve these two equations simultaneously:
2E - C = 150kg (Equation 2)
D + E - C = 180kg (Equation 1)
Adding Equation 1 and Equation 2, we get:
3E = 330kg
E = 110kg
Substituting the value of E into Equation 2, we get:
2(110kg) - C = 150kg
220kg - C = 150kg
C = 70kg
Substituting the values of E and C into Equation 1, we get:
D + 110kg - 70kg = 180kg
D = 140kg
Now, we can substitute the values of D, C, and E into the equation A + B + C = 95kg to find A and B:
A + B + 70kg = 95kg
A + B = 25kg
Since there are no additional equations involving A and B, we cannot determine their exact values.
Therefore, the weights of the five students are:
A + B = 25kg
C = 70kg
D = 140kg
E = 110kg
Community Answer
Five students went to a doctor for regular checkup. Doctor asked his ...
Let p, q, r, s, t be the weight of 5 students. Let us assume that p < q="" />< r="" />< s="" />< />
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.
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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
ample number of questions to practice 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? tests, examples and also practice CAT tests.
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