Question

21. An electric heater can boil a certain amount of water in 10 minute and another heater can
do it in 15 minute, both working at the same voltage. If the two heaters are connected in
parallel across the same voltage as before how much time will they take to boil the same
amount of water ? ​

Answer 1

An electric heater can boil a certain amount of water in 10 min.

So, in 1 min it boil water = $\sf{\frac{1}{10}}$

Another electric heater can boil water in 15 min.

Time taken by another electric heater to boil water in 1 min = $\sf{\frac{1}{15}}$

Let the -

• Time taken by both the electric heater to boil the water = x

So, In 1 min = $\sf{\frac{1}{x}}$

Both the heaters are connected in parallel across the same voltage.

We have to find the time taken by both the electric heaters to boil the water.

To find the time taken by both the electric heaters to boil the water. Simply, add the time taken by both of them in 1 min.

According to question,

=> $\sf{\dfrac{1}{10}\:+\:\dfrac{1}{15}\:=\:\dfrac{1}{x}}$

=> $\sf{\dfrac{3\:+\:2}{30}\:=\:\dfrac{1}{x}}$

=> $\sf{\dfrac{5}{30}\:=\:\dfrac{1}{x}}$

=> $\sf{\dfrac{1}{6}\:=\:\dfrac{1}{x}}$

=> $\sf{x\:=\:6}$

•°• Time taken by both the electric heaters to boil the water is 6 min.

Answer 2

AnswEr :

⋆ Water Boiled by Heater₁ in 1 min. = $\mathsf{\dfrac{1}{10}}$

⋆ Water Boiled by Heater₂ in 1 min. = $\mathsf{\dfrac{1}{15}}$

⋆ As Both Heater is connected in Parallel Series then Voltage Regulated to them will be Equal. That's Why Just Add the time taken in 1 minute by both of them and Divide by 1 to Get Total Time.

• Total Time Taken by Both Heater :

$\longrightarrow \mathsf{Time \: Taken \: by \:( Heater_1 +Heater_2) }$

$\longrightarrow \mathsf{ \dfrac{1}{10} + \dfrac{1}{15} }$

$\longrightarrow \mathsf{ \dfrac{(3 + 2)}{30} }$

$\longrightarrow \mathsf{ \cancel\dfrac{ 5}{30} }$

$\longrightarrow \mathsf{ \dfrac{1}{6} }$

⠀

$\therefore$ The time taken to boil the same amount of water when both are used in parallel is 6 min.