Ajay and Babar were scheduled to start a project at 9:00 AM in the morning, but one of them joined the work one hour after schedule, i.e., at 10:00 AM, while the other was on schedule. If it is given that, the project would be completed at 3:00 PM on the same day had Babar been late and at 2:30 PM on the same day had Ajay been late, then find the scheduled time when the project was supposed to be completed.

Let A and B be the efficiencies of Ajay and Babar, and let T be the scheduled completion time in hours from 9 AM. The first condition gives the equation A multiplied by T plus B multiplied by (T minus 1) equals the total work. The second condition gives the equation A multiplied by (T minus 1) plus B multiplied by T equals the total work. Setting these two equations equal to each other results in AT plus BT minus B equaling AT plus BT minus A, which simplifies to A equals B. Since their efficiencies are equal, the scheduled time must be exactly halfway between the two actual completion times of 5.5 hours and 5 hours. Averaging 5.5 and 5 gives a scheduled time of 5.25 hours from 9 AM. This time of 5 hours and 15 minutes corresponds to 2:15 PM. The correct answer is 2:15 PM.

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