If `(7)/(16)` of the weight of a brick is `(21)/(8)` kg, then `(5)/(12)` of the weight of the brick will be :

Options

A. `(10)/(3) kg`
B. `(3)/(5)` kg
C. `(3)/(10)` kg
D. `(5)/(2)` kg

Answer

To solve the problem step by step, we need to find the weight of the brick first and then calculate \(\frac{5}{12}\) of that weight.

### Step 1: Set up the equation
We know from the question that:
\[ \frac{7}{16} \text{ of the weight of the brick} = \frac{21}{8} \text{ kg} \]
Let the weight of the brick be \( W \). Therefore, we can write:
\[ \frac{7}{16} W = \frac{21}{8} \]

### Step 2: Solve for \( W \)
To find \( W \), we can multiply both sides of the equation by \(\frac{16}{7}\):
\[ W = \frac{21}{8} \times \frac{16}{7} \]

### Step 3: Simplify the right-hand side
Now, we can simplify the right-hand side:
\[ W = \frac{21 \times 16}{8 \times 7} \]
Calculating the numerator and denominator:
- \(21 \times 16 = 336\)
- \(8 \times 7 = 56\)

So we have:
\[ W = \frac{336}{56} \]

### Step 4: Divide to find \( W \)
Now, we can simplify \(\frac{336}{56}\):
\[ W = 6 \text{ kg} \]

### Step 5: Calculate \(\frac{5}{12}\) of the weight of the brick
Now that we have the weight of the brick, we need to find \(\frac{5}{12}\) of \( W \):
\[ \frac{5}{12} W = \frac{5}{12} \times 6 \]

### Step 6: Perform the multiplication
Calculating \(\frac{5}{12} \times 6\):
\[ \frac{5 \times 6}{12} = \frac{30}{12} \]

### Step 7: Simplify \(\frac{30}{12}\)
Now, simplify \(\frac{30}{12}\):
\[ \frac{30}{12} = \frac{5}{2} \text{ kg} \]

### Final Answer
Thus, \(\frac{5}{12}\) of the weight of the brick is:
\[ \frac{5}{2} \text{ kg} \]