Hi RiyaR,

As wordy and complex as this question might first appear, you can break it down into pieces and solve with very little in the way of tough calculations.

We're told....

Machine K took 3 hours to produce 1/4 of the units. From this, we have a rate (every 3 hours another 1/4 of the units are produced).

Machines K and M took 6 more hours to finish producing the rest of the units. Let's break this into two pieces:

Machine K worked for 6 more hours
Machine M worked for 6 hours

We know Machine K's rate: 3 hours to complete 1/4 of the units. Since it worked 6 more hours, Machine K completed 2(1/4) = 1/2 of the units during that time. Counting the initial 3 hours (and 1/4 of the units) that Machine K worked, it completed 1/4 + 1/2 = 3/4 of the units.

The remaining 1/4 of the units must have been produced by Machine M over the course of those 6 hours....

Machine M takes 6 hours to produce 1/4 of the units.

We're asked how long it would take Machine M to produce ALL of the units...

6 hours to produce 1/4 of the units =
24 hours to produce all of the units.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich