$Naimish and Pramod are two friends. A total of Rs. 1800 was paid to both of them for completing a work. Naimish started working and worked for ‘X’ days and then left and the remaining work was completed by Pramod and he was paid Rs. 1080. If Naimish and Pramod alone can complete the work in 30 days and Y days respectively. Which of the following options is /are possible for the value of 'X' and 'Y' are respectively.$ A- 12, 36 B- 12, 30 C- 12, 25 D- 16, 25

Let Naimish's 1 day work = 1/30. Let Pramod's 1 day work = 1/Y. Naimish worked X days and Pramod completed remaining work. Payment is proportional to work done. Pramod got Rs.1080 out of Rs.1800, so Pramod did 1080/1800 = 3/5 of work. Therefore Naimish did 2/5 of work in X days. X/30 = 2/5 gives X = 12. Pramod completed 3/5 of work alone, so time taken = (3/5)Y. Total work equation: X/30 + (3/5)Y/Y = 1. With X=12: 12/30 + 3/5 = 1, which holds. This works for any Y. Testing options: A (12,36), B (12,30), C (12,25) all satisfy X=12. D (16,25) gives X=16 which doesn't satisfy X/30 = 2/5.