In a house, an electric bulb of $60 W$ is used for $15 h o u r s$ and an electric heater of $750 W$ is used for $10 h o u r s$ every day. Calculate the cost of using the bulb and the heater for 30 days if the cost of 1 unit of electrical energy is $₹ 4 .$

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Solution

Step 1- Given Data and formulas
Power rating of the electric bulb $P_{1} = 60 W$
Power rating of the heater $P_{2} = 750 W$
Time of use of electric bulb in one day $t_{1} = 15 h o u r s$
Time of use of the heater in one day $t_{2} = 10 h o u r s$
Cost of 1 unit of electrical energy $r = ₹ 4$
The energy consumption of an electrical device is given by
$E = P t$
Where $E$ is the energy consumed, $t$ is the total run time of the device and $P$ is the power rating of an electrical device.
Note: $1 W = 10^{- 3} k W$
Step 2- Finding the energy consumed by the bulb
Consider $E_{1}$ be the total energy consumed by the bulb
The total energy consumed by the electric bulb is given by
$E_{1} = P_{1} t_{1} N$
Where $N$ is the number of days.
Substitute the values of power rating, number of days and $t_{1}$ into the formula to find the total energy consumed by the bulb.
$E_{1} = 60 \times 10^{- 3} k W \times 15 h o u r s / d a y \times 30 d a y s E_{1} = 27 k W h$
Step 3- Finding the energy consumed by the heater
Consider $E_{2}$ be the total energy consumed by the heater
The total energy consumed by the electric heater is given by
$E_{2} = P_{2} t_{2} N$
Where $N$ is the number of days.
Substitute the values of power rating, number of days and $t_{2}$ into the formula to find the total energy consumed by the bulb.
$E_{2} = 750 \times 10^{- 3} k W \times 10 h o u r s / d a y \times 30 d a y s E_{2} = 225 k W h$
Step 4- Finding the total energy consumed
The total energy consumed is given by
$E = E_{1} + E_{2}$
Where $E$ is the total energy consumed.
Substitute the calculated values of energies
$E = 27 k W h + 225 k W h E = 252 k W h$
Step 5- Finding the total cost
The total cost of using the bulb and the heater for 30 days is given by
$C = Er$
where $C$ is the total cost,
Substitute the value of total energy and Cost of 1 unit of electrical energy into the formula to calculate the total cost.
$C = 252 k W h \times 4 ₹ / k W h C = ₹ 1008$
Thus, the cost of using the bulb and the heater for 30 days is $₹ 1008$ .

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In a house, an electric bulb of $60 W$ is used for $15 h o u r s$ and an electric heater of $750 W$ is used for $10 h o u r s$ every day. Calculate the cost of using the bulb and the heater for 30 days if the cost of 1 unit of electrical energy is $₹ 4 .$