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. Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project?
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. Ajay and Vijay together have to complete a project. Ajay alone can c...
Problem:
Ajay alone can complete a project in 8 days, while Vijay alone can complete it in 16 days. If they work on alternate days, starting with Ajay, how many days will they take to finish the project?
Solution:
To find the number of days required to complete the project when Ajay and Vijay work alternately, we need to determine their combined efficiency.
Let's assume that the total work to be done is 16 units (LCM of 8 and 16) to make calculations easier.
Efficiency of Ajay:
Since Ajay can complete the entire project in 8 days, his daily efficiency is 1/8th of the total work.
Therefore, Ajay's efficiency = 16 units / 8 days = 2 units/day.
Efficiency of Vijay:
Similarly, since Vijay can complete the entire project in 16 days, his daily efficiency is 1/16th of the total work.
Therefore, Vijay's efficiency = 16 units / 16 days = 1 unit/day.
Combined Efficiency:
When Ajay and Vijay work alternately, Ajay works on odd-numbered days and Vijay works on even-numbered days. Since the work is divided equally between them, their combined efficiency can be calculated by summing their individual efficiencies.
Combined efficiency = Ajay's efficiency + Vijay's efficiency = 2 units/day + 1 unit/day = 3 units/day.
Time Required to Complete the Project:
To find the number of days required to complete the project, divide the total work by the combined efficiency.
Time required = Total work / Combined efficiency = 16 units / 3 units/day ≈ 5.33 days.
Therefore, Ajay and Vijay will be able to finish the project in approximately 5.33 days when they work on alternate days, starting with Ajay.
Note: Since we cannot have fractional days, we can round the answer up to the nearest whole number. In this case, the project will take 6 days to complete.
Ajay alone can complete a project in 8 days, while Vijay alone can complete it in 16 days. If they work on alternate days, starting with Ajay, how many days will they take to finish the project?
Solution:
To find the number of days required to complete the project when Ajay and Vijay work alternately, we need to determine their combined efficiency.
Let's assume that the total work to be done is 16 units (LCM of 8 and 16) to make calculations easier.
Efficiency of Ajay:
Since Ajay can complete the entire project in 8 days, his daily efficiency is 1/8th of the total work.
Therefore, Ajay's efficiency = 16 units / 8 days = 2 units/day.
Efficiency of Vijay:
Similarly, since Vijay can complete the entire project in 16 days, his daily efficiency is 1/16th of the total work.
Therefore, Vijay's efficiency = 16 units / 16 days = 1 unit/day.
Combined Efficiency:
When Ajay and Vijay work alternately, Ajay works on odd-numbered days and Vijay works on even-numbered days. Since the work is divided equally between them, their combined efficiency can be calculated by summing their individual efficiencies.
Combined efficiency = Ajay's efficiency + Vijay's efficiency = 2 units/day + 1 unit/day = 3 units/day.
Time Required to Complete the Project:
To find the number of days required to complete the project, divide the total work by the combined efficiency.
Time required = Total work / Combined efficiency = 16 units / 3 units/day ≈ 5.33 days.
Therefore, Ajay and Vijay will be able to finish the project in approximately 5.33 days when they work on alternate days, starting with Ajay.
Note: Since we cannot have fractional days, we can round the answer up to the nearest whole number. In this case, the project will take 6 days to complete.
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. Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about . Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project?.
. Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about . Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Ajay and Vijay together have to complete a project. Ajay alone can complete it in 8 days while Vijay alone requires 16 days. If both of them decide to work on alternate days, starting with Ajay, in how many days will they be able to finish the project?.
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