If the operating cost of 6 burners for 6 hours in 8 days is Rs. 450 then find the number of burners if used for 5 hours for 10 day with operating cost of Rs.1250.

Options

A. 16
B. 14
C. 12
D. 10

Answer

To solve the problem step by step, we will use the relationship between the number of burners, the hours they operate, the number of days they are used, and the operating cost.

### Step 1: Understand the given data
We have the following information:
- For the first scenario:
- Number of burners (b1) = 6
- Operating hours per day (h1) = 6
- Number of days (d1) = 8
- Total operating cost (w1) = Rs. 450

- For the second scenario:
- Number of burners (b2) = x (unknown)
- Operating hours per day (h2) = 5
- Number of days (d2) = 10
- Total operating cost (w2) = Rs. 1250

### Step 2: Set up the formula
We can use the formula that relates the two scenarios:
\[ \frac{b1 \times d1 \times h1}{w1} = \frac{b2 \times d2 \times h2}{w2} \]

### Step 3: Substitute the known values
Substituting the known values into the formula:
\[ \frac{6 \times 8 \times 6}{450} = \frac{x \times 10 \times 5}{1250} \]

### Step 4: Simplify the left side
Calculating the left side:
\[ 6 \times 8 = 48 \]
\[ 48 \times 6 = 288 \]
So, the left side becomes:
\[ \frac{288}{450} \]

### Step 5: Simplify the right side
Calculating the right side:
\[ 10 \times 5 = 50 \]
So, the right side becomes:
\[ \frac{x \times 50}{1250} \]

### Step 6: Cross-multiply
Cross-multiplying gives us:
\[ 288 \times 1250 = 450 \times x \times 50 \]

### Step 7: Calculate the left side
Calculating \(288 \times 1250\):
\[ 288 \times 1250 = 360000 \]

### Step 8: Calculate the right side
Calculating \(450 \times 50\):
\[ 450 \times 50 = 22500 \]
So, we have:
\[ 360000 = 22500x \]

### Step 9: Solve for x
To find x, divide both sides by 22500:
\[ x = \frac{360000}{22500} \]
Calculating this gives:
\[ x = 16 \]

### Step 10: Conclusion
Thus, the number of burners (b2) needed is 16.