Question

A hall is used 5 hours a day for 25 days in a month. It has 6 lamps of 100 W each and 4 fans of 15 W. The total power consumed for the month is

A. 1500 kWh
B. 100 kWh
C. 15 kWh
D. 1.5 kWh
E. None of the above

Answer 1

Hint: This is a direct question. The formula for computing the power consumed is equal to the product of the number of watts and the number of hours by 1000. We divide the product by 1000 to compute the power consumed in terms of kilowatt. The total power consumed by the hall is the sum of the power consumed by the lamps and the fans.
Formula used:
\[1\,\text{unit}=\dfrac{\text{No}\text{.}\,\text{of watts}\times \text{No}\text{.of hours}}{1000}\]

Complete answer:
From the data, we have the data as follows.
A hall is used 5 hours a day for 25 days in a month. It has 6 lamps of 100 W each and 4 fans of 15 W.
As the hall is used for 25 days, so, the total power consumed for the month will be calculated using 25 days only.
The formula used to calculate the total power consumed is given as follows.
\[1\,\text{unit}=\dfrac{\text{No}\text{.}\,\text{of watts}\times \text{No}\text{.of hours}}{1000}\]
Here, the 1 unit refers to the 1 kWh, that is,
\[1\,\text{unit}=1\,\text{kWh}\]
As we need to compute the total power consumed by the hall, so, we will add the power consumed by the lamps and the fans.
Firstly, we will compute the power consumed by the lamps. So, we have,
A hall has 6 lamps of 100 W each used 5 hours a day for 25 days.
\[\begin{align}
  & 1\,\text{unit}=\dfrac{(6\times 100)\times (5\times 25)}{1000} \\
 & \Rightarrow 1\,\text{unit}=75\,\text{kWh} \\
\end{align}\]
Therefore, the total power consumed by the lamps will be 75 kWh

Now, we will compute the power consumed by the fans. So, we have,
A hall has e fans of 50 W each used 5 hours a day for 25 days.
\[\begin{align}
  & 1\,\text{unit}=\dfrac{(4\times 50)\times (5\times 25)}{1000} \\
 & \Rightarrow 1\,\text{unit}=25\,\text{kWh} \\
\end{align}\]
Therefore, the total power consumed by the fans will be 7.5 kWh
The total power consumed by the hall is the sum of the total power consumed by the lamps and total power consumed by the fans. So, we have,
\[\begin{align}
  & 1\,\text{unit}=75\,\text{kWh}+25\,\text{kWh} \\
 & \Rightarrow 1\,\text{unit}=100\,\text{kWh} \\
\end{align}\]
.
So, the correct answer is “Option B”.

Note:
The formula, 1 unit equals 1 kWh should be known. The question statement is a bit confusing, as they have given that, “A hall is used 5 hours a day for 25 days in a month” and asked to find, “The total power consumed for the month”. So, we should not get confused with 25 days and a month.