In an exercise room some discs of denominations 2 kg and 5 kg are kept for weightlifting. If the total number of discs is 21 and the weight of all the discs of 5 kg is equal to the weight of all the discs of 2 kg, find the weight of all the discs together.

Options

A. 80 kg
B. 90 kg
C. 56 kg
D. None of these

Answer

To solve the problem step by step, we will define variables, set up equations based on the information given, and then solve for the total weight of the discs.

### Step 1: Define Variables
Let:
- \( A \) = number of 5 kg discs
- \( B \) = number of 2 kg discs

### Step 2: Set Up the Equations
From the problem, we know two things:
1. The total number of discs is 21:
\[ A + B = 21 \quad \text{(Equation 1)} \]

2. The total weight of the 5 kg discs is equal to the total weight of the 2 kg discs:
\[ 5A = 2B \quad \text{(Equation 2)} \]

### Step 3: Solve for One Variable
From Equation 1, we can express \( A \) in terms of \( B \):
\[ A = 21 - B \quad \text{(Substituting into Equation 1)} \]

### Step 4: Substitute into the Second Equation
Now substitute \( A \) from Equation 1 into Equation 2:
\[ 5(21 - B) = 2B \]
Expanding this gives:
\[ 105 - 5B = 2B \]

### Step 5: Combine Like Terms
Now, combine the terms involving \( B \):
\[ 105 = 2B + 5B \]
\[ 105 = 7B \]

### Step 6: Solve for \( B \)
Now, divide both sides by 7 to find \( B \):
\[ B = \frac{105}{7} = 15 \]

### Step 7: Find \( A \)
Now substitute \( B \) back into Equation 1 to find \( A \):
\[ A = 21 - B = 21 - 15 = 6 \]

### Step 8: Calculate Total Weight
Now we can calculate the total weight of all the discs:
- Weight of 5 kg discs:
\[ \text{Weight of 5 kg discs} = 5A = 5 \times 6 = 30 \text{ kg} \]
- Weight of 2 kg discs:
\[ \text{Weight of 2 kg discs} = 2B = 2 \times 15 = 30 \text{ kg} \]

### Step 9: Total Weight
Now, add the weights of both types of discs:
\[ \text{Total Weight} = 30 \text{ kg} + 30 \text{ kg} = 60 \text{ kg} \]

### Final Answer
The total weight of all the discs together is **60 kg**.

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