Given:

Alpha and Beta can finish the task in 18 days; Beta and Gama can do it in 24 days while Gama and Alpha can finish it in 36 days.

Calculation:

Time taken by (Alpha + Beta) to finish the work = 18 days

So, (Alpha + Beta)’s 1 day work = 1/18     ----(1)

Time taken by (Beta + Gama) to finish the task = 24 days

So, (Beta = Gama)’s 1 day work = 1/24     ----(2)

Time taken by (Gama + Alpha) to finish the work = 36 days

So, (Gama + Beta)’s 1 day work = 1/36      ----(3)

On adding eq. (1), (2) and (3), we have

2(Alpha + Beta + Gama)’s 1 day work = 1/18 + 1/24 + 1/36 = (4 + 3 + 2)/72 = 9/72 = 1/8

Also, (Alpha + Beta + Gama)’s 1 day work = 1/(2 × 8) = 1/16

So, Alpha, Beta, Gama together can make a sports car in 16 days.

Now, Alpha’s 1 day’s work = {(Alpha + Beta + Gama)’s 1 day’s work – (Beta + Gama)’s 1 day’s work} = 1/16 – 1/24 = (3 - 2)/48 = 1/48

Hence, Alpha alone can make the car in 48 days.

Beta 1 day’s work = {(Alpha + Beta + Gama)’s 1 day’s work – (Gama + Alpha)’s 1 day’s work}

= 1/16 – 1/36 = (9 - 4)/144 = 5/144

Hence, Beta alone can make the sports car in 144/5 days.

Gama’s 1 day’s work = {(Alpha + Beta + Gama)’s 1 day’s work – (Alpha + Beta)’s 1 day’s work}

= 1/16 – 1/18 = (9 - 8)/144 = 1/144

Hence, Gama alone can make the sports car in 144 days.

∴ Alpha, Beta and Gama alone can finish the task in 48 days, 144/5 days and 144 days respectively.