Math Problem Statement
The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, WI , of Section I is smaller than the average weight WII , of the Section II. If the heaviest student say Deepak, of section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes WII and that of Section II becomes WI . What is the weight of Poonam?
Solution
Let’s solve this problem step-by-step.
Step 1: Setting up the Equations
We know:
- The total weight of all 100 students is .
- Let the average weight of Section I be and the average weight of Section II be .
- The number of students in each section is 50.
So, the total weight of Section I is , and the total weight of Section II is .
Since the sum of the weights of both sections is the total weight of the class: Dividing both sides by 50:
Step 2: Weight Swapping
When the heaviest student, Deepak, from Section II is moved to Section I, and the lightest student, Poonam, from Section I is moved to Section II, the average weights of the sections are switched. This implies:
- The new average weight of Section I becomes .
- The new average weight of Section II becomes .
Let’s denote:
- as Deepak's weight.
- as Poonam's weight.
Step 3: Expressing the Weight Change in Each Section
For Section I:
- Initial total weight = .
- After Deepak joins and Poonam leaves, the new total weight becomes .
- The new average weight of Section I is , so: Simplifying, we get:
For Section II:
- Initial total weight = .
- After Poonam joins and Deepak leaves, the new total weight becomes .
- The new average weight of Section II is , so: Simplifying, we get:
Step 4: Solving the Equations
Now we have two equations:
Adding these two equations, we get:
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Math Problem Analysis
Mathematical Concepts
Algebra
Averages
Systems of Equations
Formulas
Average weight = Total weight / Number of students
WI + WII = 90
(50 * WI + d - p) / 50 = WII
(50 * WII + p - d) / 50 = WI
Theorems
Basic properties of averages and algebraic equations
Suitable Grade Level
Grades 10-12
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