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Understanding the Object Weights Problem
This problem asks us to find the second heaviest object among five objects: E, F, G, H, and K. We are given several relationships between their weights and the exact weight of one object (G). To solve this, we need to use the given information to determine the weights of all objects and then compare them.
Step-by-Step Weight Calculation
Let's denote the weight of an object by its letter with a subscript, e.g., \(W_E\) for the weight of object E.
- We are given that the weight of G is 7.5 kg.
\( W_G = 7.5 \text{ kg} \) - We are told that the weights of F and G are equal.
\( W_F = W_G \)
So, \( W_F = 7.5 \text{ kg} \) - The weight of E is twice the weight of F.
\( W_E = 2 \times W_F \)
Substitute the value of \(W_F\): \( W_E = 2 \times 7.5 \text{ kg} \)
So, \( W_E = 15 \text{ kg} \) - The weight of K is 4 times the weight of G.
\( W_K = 4 \times W_G \)
Substitute the value of \(W_G\): \( W_K = 4 \times 7.5 \text{ kg} \)
So, \( W_K = 30 \text{ kg} \) - The weight of H is 3 times the weight of K.
\( W_H = 3 \times W_K \)
Substitute the value of \(W_K\): \( W_H = 3 \times 30 \text{ kg} \)
So, \( W_H = 90 \text{ kg} \)
Summary of Object Weights
Let's list the calculated weights for all five objects:
- Weight of E (\(W_E\)): 15 kg
- Weight of F (\(W_F\)): 7.5 kg
- Weight of G (\(W_G\)): 7.5 kg
- Weight of H (\(W_H\)): 90 kg
- Weight of K (\(W_K\)): 30 kg
Comparing Weights to Find the Second Heaviest
Now, we need to arrange the objects in descending order of their weights to find the second heaviest object. The weights are:
- H: 90 kg
- K: 30 kg
- E: 15 kg
- F: 7.5 kg
- G: 7.5 kg
Ordering the weights from heaviest to lightest:
- H (90 kg) - Heaviest
- K (30 kg) - Second Heaviest
- E (15 kg)
- F and G (7.5 kg)
Based on this comparison, the second heaviest object is K, with a weight of 30 kg.
| Object | Weight (kg) | Weight Ranking |
|---|---|---|
| H | 90 | 1st (Heaviest) |
| K | 30 | 2nd (Second Heaviest) |
| E | 15 | 3rd |
| F | 7.5 | 4th (Jointly) |
| G | 7.5 | 4th (Jointly) |
Therefore, object K is the second heaviest.
Revision Table: Key Information from the Question
| Relationship | Formula |
|---|---|
| Weight of H is 3 times the weight of K | \(W_H = 3 \times W_K\) |
| Weight of G is 7.5 kg | \(W_G = 7.5 \text{ kg}\) |
| Weight of E is twice the weight of F | \(W_E = 2 \times W_F\) |
| Weight of K is 4 times the weight of G | \(W_K = 4 \times W_G\) |
| Weights of F and G are equal | \(W_F = W_G\) |
Additional Information: Solving Word Problems
Solving word problems involving quantities often requires translating the relationships described in text into mathematical equations or expressions. Here are some tips:
- Read Carefully: Understand exactly what is being asked and what information is provided. Identify the unknowns and the given values.
- Assign Variables: Use letters or symbols to represent the unknown quantities.
- Write Equations: Translate the relationships given in the text into mathematical equations using the variables.
- Solve Equations: Use algebraic techniques to solve for the unknown variables. If there are multiple unknowns, you might need a system of equations.
- Check Your Answer: Once you find a solution, plug the values back into the original relationships or context of the problem to ensure they make sense and satisfy all conditions.
- State the Final Answer: Make sure your final answer directly addresses the question asked in the problem.
In this specific weight comparison problem, by systematically using each piece of information, we could calculate the individual weights and then easily compare them to find the second heaviest object.
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Important Questions from Quant Based Puzzle
- There are deers and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there?
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- A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has". A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
- A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold?
There are fourteen teams playing in a tournament. If every team plays one match with every other team, how many matches will be played in the tournament?
