Question

In a factory 10 bulbs of 100w each and 5 fans of 110w each operate for 12 hours daily. Calculate the units of electricity consumed. Also find the total expenditure unit costs rupees 2

Answer 1

Answer

• Total Electrical energy consumed is 18.6 kWh
• Total cost is ₹37.2

Explanation

Given

• There are 10 bulbs of Power 100 w and 5 fans of Power 110 w each
• They work for 12 hours daily

To Find

• Electrical Energy consumed
• Cost if 1 unit = ₹2

Solition

• We know that E = P×t. So on simpe substitution we may find the electrical energy consumed by one bulb and one fan, then multiply them with the total number of fans and bulbs a d their sum will be the total energy consumed!!
• But before that we have to convert the power from Watts to Kilowatt

✭ Converting W → kW

• Bulbs : 100 W = 100/1000 = 0.1 kW
• Fan : 110 W = 110/1000 = 0.11 kW

✭ Energy Consumed by Bulbs

→ Energy = Power × Time

→ E = 0.1 × 12

→ E (bulb) = 1.2 kWh

So then for 10 such bulbs,

→ E (bulb) = 1.2 × 10

→ E (bulb) = 12 kWh

✭ Energy Consumed by Fans

→ Energy = Power × Time

→ E = 0.11 × 12

→ E (fan) = 1.32 kWh

So then for 15 such bulbs,

→ E (fan) = 1.2 × 5

→ E (fan) = 6.6 kWh

✭ Total Electrical Energy Consumed

→ E(fan) + E (bulb) = E{net}

→ 12+6.6

→ 18.6 kWh

✭ Total Cost

→ 18.6 × 2

→ Cost = ₹37.2

Answer 2

Given:-

• In a factory 10 bulbs of 100w each and 5 fans of 110w each operate for 12 hours daily.

• Cost if 1 unit = Rs 2

To Find:-

• Units of electricity consumed.

• The total expenditure

Solution:-

We know that,

$\bigstar\:\:\sf{Power =\dfrac{Energy}{Time} }$

So,

$\bigstar\:\:\sf{Energy =Power \times Time }$

Bulb :-

$\purple{\hookrightarrow\:\:}$ Power of one Bulb = 100 W

Now we convert W to kW,

[ 1kw = 1000 W ]

$\purple{\hookrightarrow\:\:}$ $\sf{100\:W=\dfrac{100}{1000}=0.1\:kW }$

$\purple{\hookrightarrow\:\:}$ Time = 12 hrs

Energy consumed by bulbs,

$\pink{\hookrightarrow\:\:}$ $\sf{E = 0.1 \times 12}$

$\pink{\hookrightarrow\:\:}$ $\sf{E = 1.2\: kWh }$

Now for ten bulbs,

$\pink{\hookrightarrow\:\:}$ $\sf{E =1.2 \times 10 }$

$\pink{\hookrightarrow\:\:}$ $\sf{E =12 \:kWh }$

Fans :-

$\purple{\hookrightarrow\:\:}$ Power of 1 fan = 110 W

Now we convert W to kW,

[ 1kw = 1000 W ]

$\purple{\hookrightarrow\:\:}$ $\sf{110\:W=\dfrac{110}{1000} =0.11\:kW}$

$\purple{\hookrightarrow\:\:}$ Time = 12 hrs

Energy consumed by funs,

$\red{\hookrightarrow\:\:}$ $\sf{E = 0.11 \times 12}$

$\red{\hookrightarrow\:\:}$ $\sf{E = 1.32\: kWh}$

Now for 15 such bulbs,

$\red{\hookrightarrow\:\:}$ $\sf{E = 1.2 \times 5}$

$\red{\hookrightarrow\:\:}$ $\sf{E =6.6\: kWh }$

Total energy consumed :-

$\orange{\hookrightarrow\:\:}$ Energy consumed by 10 bulbs + Energy consumed by 5 bulbs.

$\orange{\hookrightarrow\:\:}$ $\sf{12 + 6.6}$

$\orange{\hookrightarrow\:\:}$ $\sf{18 .6 \: kWh}$

Total Cost :-

We know that,

$\bigstar\:\:$ 1 kwh = 1 unit.

$\blue{\hookrightarrow\:\:}$ Total units of energy consumed = 18.6 units.

$\blue{\hookrightarrow\:\:}$ Cost of energy for 1 unit = Rs 2

$\blue{\hookrightarrow\:\:}$ $\sf{Total\:cost = 18.6 \times 2}$

$\blue{\hookrightarrow\:\:}$ $\sf{Total\:cost =Rs \:37.2 }$

_____________________________________