A, B and C can complete a job in 5 days. B, C and D can complete the same job in 10 days. C, D and A can complete the same job in 15 days and D, A and B can complete the same job in 30 days. How long A, B, C and D together will take to finish the job?

Correct option is C

Given:
Work done by A + B + C = 5 days
Work done by B + C + D = 10 days
Work done by C + D + A = 15 days
Work done by D + A + B = 30 days
Solution:  ​

Work rates :

A + B + C =  $$\frac{1}5$$​​

B + C + D = $$\frac{ 1}{10}$$​

C + D + A =  $$\frac{1}{15}$$​

D + A + B = $$\frac{ 1}{30}$$​​
Adding all above equations,
3(A + B + C + D) = $$\frac{1}5 + \frac{1}{10} +\frac 1{15} + \frac1{30}$$ ​

3(A + B + C + D)= $$\frac 6{30}​+\frac3{30}​+\frac 2{30}+\frac1{30}$$​

3(A + B + C + D) =$$\frac{ 12}{30}$$​​

(A + B + C + D) = $$\frac{2}{15}$$​​
Now , working together all four can complete the work in :

​$$\frac{1}{2/15} = \frac{15}{2}= 7\frac{1}{2} \ days$$​​
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