The expenditure on gas is ₹ 450. If 6 burners light for 8 days for 6 hours per day. How many burners are required to expense ₹625, 5 hours lighting per day for 10 days?

Options

A. 5 burners
B. 8 burners
C. 9 burners
D. 10 burners

Answer

To solve the problem step by step, we will use the relationship between the number of burners, time, days, and expenditure.

### Step 1: Understand the given information
We know that:
- Expenditure for 6 burners for 8 days at 6 hours per day is ₹450.
- We need to find how many burners (let's call it X) are required for an expenditure of ₹625, lighting for 5 hours a day for 10 days.

### Step 2: Set up the relationship
We can use the formula based on the relationship of work done:
\[ \frac{M_1 \times T_1 \times D_1}{W_1} = \frac{M_2 \times T_2 \times D_2}{W_2} \]
Where:
- \( M_1 = 6 \) (initial number of burners)
- \( T_1 = 6 \) (initial hours per day)
- \( D_1 = 8 \) (initial days)
- \( W_1 = 450 \) (initial expenditure)
- \( M_2 = X \) (unknown number of burners)
- \( T_2 = 5 \) (new hours per day)
- \( D_2 = 10 \) (new days)
- \( W_2 = 625 \) (new expenditure)

### Step 3: Substitute the values into the formula
Substituting the known values into the formula gives us:
\[ \frac{6 \times 6 \times 8}{450} = \frac{X \times 5 \times 10}{625} \]

### Step 4: Simplify the left side
Calculating the left side:
\[ \frac{6 \times 6 \times 8}{450} = \frac{288}{450} = \frac{32}{50} = \frac{16}{25} \]

### Step 5: Simplify the right side
Now, simplifying the right side:
\[ \frac{X \times 5 \times 10}{625} = \frac{50X}{625} = \frac{X}{12.5} \]

### Step 6: Set the two sides equal
Now we set the two sides equal to each other:
\[ \frac{16}{25} = \frac{X}{12.5} \]

### Step 7: Cross-multiply to solve for X
Cross-multiplying gives us:
\[ 16 \times 12.5 = 25X \]
Calculating \( 16 \times 12.5 \):
\[ 200 = 25X \]

### Step 8: Solve for X
Now, divide both sides by 25:
\[ X = \frac{200}{25} = 8 \]

### Conclusion
Thus, the number of burners required is **8**.

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