Questions :
A can lay a railway track between two stations in 20 days, B can complete the same task in 15 days, and C assists them to finish the job in 5 days. How long would it take for C alone to complete the job?
Options :
- 8 days
- 10 days
- 12 days
- 13 days
correct answer : c)
Explanation :
A’s work rate = 1/20
B’s work rate = 1/15
(A + B + C)’s combined work rate = 1/5
C’s work rate = 1/5 − (1/20 + 1/15)
= 1/5 − 7/60
= 12/60 − 7/60
= 5/60
= 1/12
Therefore, the time taken by C alone to complete the work = 1 ÷ (1/12) = 12 days.
Hence, the correct answer is option (c) 12 days. The options 8 days, 10 days, and 13 days are incorrect because C’s individual work rate is 1/12 of the work per day, which means C requires exactly 12 days to complete the entire job alone.