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The following are the weights of five students p, Q, R, s, t taken three at a time 125kg, 127kg, 128kg, 132kg, 133kg, 135kg, 135kg, 136kg, 138kg and143kg.the weight of each of the students is a distinct integer.it is known that T is the heaviest and p, Q and s together weighted 16 kg less than R, S and T together question who is the third heaviest student Who is the weight of heaviest student?
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Most Upvoted Answer
The following are the weights of five students p, Q, R, s, t taken thr...
Solution:

Given data:
- Weights of students taken three at a time: 125kg, 127kg, 128kg, 132kg, 133kg, 135kg, 135kg, 136kg, 138kg and 143kg
- T is the heaviest student
- P, Q and S together weighed 16 kg less than R, S and T together

Let's solve this question step-by-step.

Step 1: Find the sum of all weights
- Sum of weights taken three at a time: 125kg + 127kg + 128kg + 132kg + 133kg + 135kg + 135kg + 136kg + 138kg + 143kg = 1352kg
- Let's assume the weight of P, Q, R, S, and T as x1, x2, x3, x4, and x5 respectively.
- Sum of all weights: x1 + x2 + x3 + x4 + x5 = (125+127+128+132+133+135+135+136+138+143) + (x1+x2+x3+x4+x5)
=> x1 + x2 + x3 + x4 + x5 = 1551kg

Step 2: Find the heaviest student
- T is the heaviest student, i.e., x5 = 143kg

Step 3: Use the given condition to form an equation
- P, Q, and S together weighed 16 kg less than R, S, and T together
=> x1 + x2 + x4 = x3 + x4 + x5 - 16
=> x1 + x2 = x3 + x5 - 16 - x4
- We know that x5 is the heaviest student, so x3 and x4 are the next two heaviest students.
- From the above equation, we can say that the sum of the weights of P and Q is less than the sum of the weights of R and T by (16 + x4) kg.
- So, the weight of P and Q cannot be greater than the weight of R and T. Hence, x1 + x2 < x3="" +="" />

Step 4: Use the above conditions to find the weight of each student
- As the sum of all weights is 1551kg, we can subtract the weight of T from it to get the sum of the weights of P, Q, R, and S.
=> x1 + x2 + x3 + x4 = 1551 - 143 = 1408kg
- As we know that x1 + x2 < x3="" +="" x5,="" we="" can="" assume="" the="" following="" />
* (x1 + x2) = (x3 + x4) = 469kg and x5 = 143kg (since x1, x2, x3, x4, and x5 are distinct integers)
* (x1 + x2) = (x3 + x4) = 470kg and x5 = 143kg
* (x1 + x2) = (x3 + x4) = 471kg and x5 = 143kg
* (x1 + x2) = (
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The following are the weights of five students p, Q, R, s, t taken three at a time 125kg, 127kg, 128kg, 132kg, 133kg, 135kg, 135kg, 136kg, 138kg and143kg.the weight of each of the students is a distinct integer.it is known that T is the heaviest and p, Q and s together weighted 16 kg less than R, S and T together question who is the third heaviest student Who is the weight of heaviest student?
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