Question

An air conditioner can cool the hall in $40minutes$ while another takes $45minutes$to cool under similar conditions. If both air conditioners are switched on at the same instance then how long will it take to cool the room approximately?

• A. $18min$
• B. $19min$
• C. $22min$
• D. $24min$

Answer 1

The correct option is C

$22min$

Correct option: (c )$22min$

Let the two conditioners be $A$ and $B$

• Air conditioner$A$ cools at $40minutes$
• Air conditioner $B$ at $45minutes$

We know that,

$capacity=\frac{1}{timetakentocoolthehall}$

We have,

The capacity of $A=\frac{1}{40}$ and capacity of $B=\frac{1}{45}$

So, when both the air conditioners are turned on at the same time, the combined capacity will be the addition of the capacity of both the air conditioners.

So, the combined capacity of $A$ and $B$ is $\frac{1}{40}+\frac{1}{45}=\frac{\left(45+40\right)}{\left(40\times 45\right)}$

Now, we know that

$Timetaken=\frac{1}{combinedcapacity}$

$\begin{array}{rcl}& =& \frac{(45x45)}{\left(45+40\right)}\\ & =& \frac{1800}{45}\\ & =& 21.1764\\ & =& 22min\left(approximately\right).\end{array}$

The air conditioner$A$ and air conditioner $B$ together take approximately$22min$ to cool the room.

Hence, option C is correct.