Question

Anil, Bhuvan and Chandan take 10, 20, and 25 days to complete a job. What is the minimum time required to finish the job if not more than two of them work together on a single day and no two consecutive days have the same pair of people working?

• A. 6.5 days
• B. $6\frac{13}{15}$ days
• C. 7.5 days
• D. $7\frac{21}{28}$ days

Answer 1

The correct option is B $6\frac{13}{15}$ days

Assume total amount of work = 100 units.
A does = 10 units/day, B does = 5 units/day, and C does = 4 units/day
Possible Pairs:
A+B = 15 units/day, A+C = 14 units/day, B+C = 9 units/day
To minimize time, we will use the first two pairs.
So, 15 +14 +15 + 14 + 15 +14 + 15 = 102 units.
So, little less than 7 days are required
Hence, option (b) is correct answer.