An AC can cool a hall in 10min, while an AC of another brand can cool the same hall in 15min. If both the ACs are switched on at the same time, then in how much time will they cool the hall?

Let the two AC units be A and B.
Time taken by AC A=10minutes

Time taken by AC B=15minutes

Let the total cooling work required be the LCM of 10 and 15, which is 30 units.

Cooling rate (efficiency) of AC A=
10
30
​
=3units/min

Cooling rate (efficiency) of AC B=
15
30
​
=2units/min

When both ACs work together, their combined cooling rate is:

Combined Rate=3+2=5units/min
The time taken by both ACs to complete the work is:

Time=
Combined Rate
Total Work
​
=
5
30
​
=6minutes