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A group of 10 people can finish a certain work in 15 days. If a group of 5 people who are 30% more efficient are added to the group, how many days approximately will be saved?
- A12 days
- B3 days
- C9 days
- D6 days
Answer not set
Discussion 1
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CCommunity
Let the total amount of work be X
Work done by one person in 15 days = X/10
Work done by one person in one day = X/150
A person who is 30% more efficient will be able to do 30% more work in one day.
Work done by more efficient person in one day = (1 + 0.3) × (X/150) = 1.3X/150
Now in total there are 15 people in the group and hence we have 10 persons who can finish X/150 work in one day and 5 who can finish 1.3X/150 in one day.
Total work that can be finished in one day = 10 × (X/150) + 5 × (1.3X/150) = 16.5X/150
∴ Time taken to finish the work = 150/16.5 = 9.09 days = 9 days
∴ Days saved = 15 - 9 = 6 days
Work done by one person in 15 days = X/10
Work done by one person in one day = X/150
A person who is 30% more efficient will be able to do 30% more work in one day.
Work done by more efficient person in one day = (1 + 0.3) × (X/150) = 1.3X/150
Now in total there are 15 people in the group and hence we have 10 persons who can finish X/150 work in one day and 5 who can finish 1.3X/150 in one day.
Total work that can be finished in one day = 10 × (X/150) + 5 × (1.3X/150) = 16.5X/150
∴ Time taken to finish the work = 150/16.5 = 9.09 days = 9 days
∴ Days saved = 15 - 9 = 6 days