A is 50% more efficient than B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in approximately:

Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Answer 1

Assume the work has 40 units in total, matching C's 40 day schedule so C completes 1 unit every day. Since C's daily output is half of A and B's combined daily output, A and B together must finish 2 units per day, meaning A and B together would need 20 days for the whole job. A works 50% faster than B, so their 2 units per day split as B doing 0.8 units and A doing 1.2 units, since $1.2 = 1.5 \times 0.8$ and $1.2+0.8=2$. Adding C's 1 unit per day, all three together complete $1.2+0.8+1 = 3$ units per day. To finish 40 units at 3 units per day takes $40/3$ days, close to 13.3 days. $\boxed{\text{approximately 13 days}}$

A is 50% more efficient than B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in approximately:

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The Correct Option is A

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