A and B together can complete a task in 20 days. B and C together can complete the same task in 30 days. A and C together can complete the same task in 40 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone ?

Let a, b, c be the amount of work done by A, B, C in 1 day and the total work be W units

(a+b) 20 = (b+c) 30 = (a+c) 40 = W

(a+b) 2 = (b+c) 3 = (a+c) 4 

2a+2b = 3b+3c

b = 2a-3c

2a+2b = 4a+4c

2b = 2a+4c

2(2a-3c) = 2a+4c

2a=10c

a=5c

Number of days taken by A to complete the work = $$\ \frac{\ W}{a}$$

Number of days taken by C to complete the work = $$\ \frac{\ W}{c}$$

Required ratio = $$\ \frac{\ \ \frac{\ w}{a}}{\ \frac{\ w}{c}}$$

= 1:5

D is the correct answer.