Final answer:
Rahul, Ved, and Vedaihi contributed to the project based on their efficiencies. Ved was 20% more efficient than Vedaihi and completed a greater share of work. Rahul's share of the Rs.14400 payment for the project is Rs.4500, considering his equal efficiency to Vedaihi and 31.25% of the total work contribution.
Step-by-step explanation:
To find the share of Rahul from the Rs.14400 project completed together by Rahul, Ved, and Vedaihi in 36 days, we need to understand their individual contribution to the completion of the project. Since it is given that Ved is 20% more efficient than Vedaihi, we can infer that if Vedaihi's efficiency is 100 units, then Ved's efficiency is 120 units.
It is also given that Rahul and Vedaihi together can complete the same work in 72 days. We can assume the efficiency of Rahul and Vedaihi together to be 14400 / 72 = 200 units per day. Since Vedaihi's efficiency is 100 units per day and the combined efficiency is 200 units per day, Rahul's individual efficiency is 200 units - 100 units = 100 units per day.
Now, let's find the individual contributions during the 36 days. Vedaihi's work is 36 days * 100 units/day = 3600 units, Ved's work is 36 days * 120 units/day = 4320 units, and Rahul's work is 36 days * 100 units/day = 3600 units. The total work done is 3600 + 4320 + 3600 = 11520 units. Rahul's percentage of work is 3600 / 11520 = 0.3125 or 31.25%. Rahul's share of the total payment is thus 31.25% of Rs.14400, which equals to Rs.4500.