Question

A $400\,W$refrigerator operates for $16$ hours per day. Calculate the cost to operate it for $30$ days at $Rs\,3.40\,per\,kWh$.

Answer 1

Hint: In the given question, we are given the power of a refrigerator and the time duration for which it is used in a single day. Also, we are given the cost of the each kWh of electricity used to run the refrigerator. So, we have to calculate the cost of operating the refrigerator for $30$ days with the help of information given to us in the problem itself.

Complete step by step answer:
In the question, we are given the power of the refrigerator as $400\,W$. Time duration for which the refrigerator is used each day is $16$ hours. We know that Power is the amount of energy that is spent per unit time. So, we can obtain the total amount of energy used by the refrigerator in a day by multiplying the power of the refrigerator with the time duration it is used each day.

So, total energy used by the refrigerator in a day $ = \left( {400W} \right)\left( {16hrs} \right) = 6,400Wh$
Now, total energy used in $30$ such days can be calculated by multiplying the energy consumption of a single day with $30$.
So, the total energy used by refrigerator in $30$ days $ = 6400Wh \times 30= 1,92,000Wh$
Converting the total amount of energy used in $30$ days from Wh to kWh, we get $192\;kWh$. Now, we are given the rate of energy per unit kWh as $Rs\,3.40\,per\,kWh$.
So, the cost of operating the refrigerator for $30$ days $ = 192kWh \times Rs\,3.4/kWh$
Therefore, the cost of operating the refrigerator for $30$ days $ = Rs\,652.8$

Hence, the cost of operating a $400\,W$ refrigerator operating for $16$ hours per day for $30$ days is $Rs\,652.8$.

Note:The given question is a numerical that revolves around the concepts of power and energy. One must know the formulae for the evaluation of power and energy in order to solve such questions with ease. One should also take care while doing calculations.Calculations should be checked twice in order to be sure of the answer.