Aman, Bharat and Chirag are hired to complete a project. Aman and Bharat together can complete the project in 24 days, while Bharat and Chirag together can complete it in 30 days. To finish the project, Aman worked for 12 days, Bharat worked for 24 days and Chirag worked for 30 days. Find the time taken by Aman alone to complete the project.

ATQ, Let Aman’s 1-day work be a. Let Bharat’s 1-day work be b. Let Chirag’s 1-day work be c. Aman and Bharat together complete the project in 24 days. So, a + b = 1/24 Bharat and Chirag together complete the project in 30 days. So, b + c = 1/30 From a + b = 1/24: b = 1/24 − a From b + c = 1/30: c = 1/30 − b c = 1/30 − (1/24 − a) c = 1/30 − 1/24 + a 1/30 − 1/24 = (4 − 5)/120 = −1/120 So, c = a − 1/120 Total work done by all three: 12a + 24b + 30c = 1 Put the values of b and c: 12a + 24(1/24 − a) + 30(a − 1/120) = 1 12a + 1 − 24a + 30a − 30/120 = 1 30/120 = 1/4 So, 12a − 24a + 30a + 1 − 1/4 = 1 18a + 3/4 = 1 18a = 1 − 3/4 18a = 1/4 a = 1/(4 × 18) a = 1/72 So, Aman alone can complete the project in 72 days