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Three persons a ,b and c decide to work in such a way that a and c work together on 1st day ,b alone on 2 nd day , a and c on 3 rd and so on on alternate days .how many days will be required to complete the whole work if c and d alone finished the whole work in 20 days and 34 days respectively and b is 70% more efficient than D but 20% less efficient than A?
Verified Answer
Three persons a ,b and c decide to work in such a way that a and c wor...
Ans.
Method to Solve :
work is done by B in = 100/170 * 34
=20 days
work is done by A in = 100/80 * 20
= 25 days
A=1/25: B=1/20: c=1/20.
1st day - A+C = 1/25 + 1/20 = 9/100
2nd day B = 1/20
so one pair of days work done = 9/100 + 1/20
= 14/100 = 7/50
7 pairs of days (or) 14 days of work done is = 7 * 7/50 = 49/50
Remaining work = 1 - 49/50
= 1/50
so 15 th days is A tern..
A's one day work 1/25
1/50 of work is done by A in = 1/50 * 25 = 1/2 days
total time taken 14 (1/2) days
=20 days
work is done by A in = 100/80 * 20
= 25 days
A=1/25: B=1/20: c=1/20.
1st day - A+C = 1/25 + 1/20 = 9/100
2nd day B = 1/20
so one pair of days work done = 9/100 + 1/20
= 14/100 = 7/50
7 pairs of days (or) 14 days of work done is = 7 * 7/50 = 49/50
Remaining work = 1 - 49/50
= 1/50
so 15 th days is A tern..
A's one day work 1/25
1/50 of work is done by A in = 1/50 * 25 = 1/2 days
total time taken 14 (1/2) days
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Most Upvoted Answer
Three persons a ,b and c decide to work in such a way that a and c wor...
Given Information:
- Person C can complete the work in 20 days.
- Person D can complete the work in 34 days.
- Person B is 70% more efficient than D.
- Person B is 20% less efficient than A.
Efficiency Comparison:
Let's assume that person D's efficiency is 1 unit of work per day.
- Person B's efficiency would be 1 + 70% of 1 = 1 + 0.7 = 1.7 units of work per day.
- Person A's efficiency would be 1.7 + 20% of 1.7 = 1.7 + 0.34 = 2.04 units of work per day.
Work Calculation:
Let's assume the total work to be done is represented by W.
- Person C can complete the work in 20 days, so in one day, person C completes W/20 units of work.
- Person D can complete the work in 34 days, so in one day, person D completes W/34 units of work.
- Person B is 70% more efficient than D, so in one day, person B completes 1.7(W/34) units of work, which simplifies to W/20 units of work.
- Person A is 20% less efficient than A, so in one day, person A completes 0.8(2.04(W/20)) units of work, which simplifies to W/25 units of work.
Work Distribution:
Based on the given condition, persons A and C work together on alternate days, while person B works alone on the other days.
- On the first day, A and C work together and complete (W/20) + (W/20) = W/10 units of work.
- On the second day, B works alone and completes W/20 units of work.
- On the third day, A and C work together and complete (W/20) + (W/20) = W/10 units of work.
- This alternating pattern continues.
Work Completion Calculation:
Let's calculate the work completed in each 3-day cycle.
- In the first 3 days, the work completed is (W/10) + (W/20) + (W/10) = 6W/20 = 3W/10 units of work.
- In the second 3 days, the work completed is (W/10) + (W/20) + (W/10) = 3W/10 units of work.
- This pattern repeats every 3 days.
Total Days to Complete the Work:
Since the work completion pattern repeats every 3 days, we can calculate the number of 3-day cycles required to complete the entire work.
Total work = W
Work completed in each 3-day cycle = 3W/10
Number of 3-day cycles required = W / (3W/10) = 10/3
Therefore, the whole work will be completed in 10/3 cycles of 3 days each.
Final Answer:
To complete the whole work, it will take 3 x (10/3) = 10 days.
- Person C can complete the work in 20 days.
- Person D can complete the work in 34 days.
- Person B is 70% more efficient than D.
- Person B is 20% less efficient than A.
Efficiency Comparison:
Let's assume that person D's efficiency is 1 unit of work per day.
- Person B's efficiency would be 1 + 70% of 1 = 1 + 0.7 = 1.7 units of work per day.
- Person A's efficiency would be 1.7 + 20% of 1.7 = 1.7 + 0.34 = 2.04 units of work per day.
Work Calculation:
Let's assume the total work to be done is represented by W.
- Person C can complete the work in 20 days, so in one day, person C completes W/20 units of work.
- Person D can complete the work in 34 days, so in one day, person D completes W/34 units of work.
- Person B is 70% more efficient than D, so in one day, person B completes 1.7(W/34) units of work, which simplifies to W/20 units of work.
- Person A is 20% less efficient than A, so in one day, person A completes 0.8(2.04(W/20)) units of work, which simplifies to W/25 units of work.
Work Distribution:
Based on the given condition, persons A and C work together on alternate days, while person B works alone on the other days.
- On the first day, A and C work together and complete (W/20) + (W/20) = W/10 units of work.
- On the second day, B works alone and completes W/20 units of work.
- On the third day, A and C work together and complete (W/20) + (W/20) = W/10 units of work.
- This alternating pattern continues.
Work Completion Calculation:
Let's calculate the work completed in each 3-day cycle.
- In the first 3 days, the work completed is (W/10) + (W/20) + (W/10) = 6W/20 = 3W/10 units of work.
- In the second 3 days, the work completed is (W/10) + (W/20) + (W/10) = 3W/10 units of work.
- This pattern repeats every 3 days.
Total Days to Complete the Work:
Since the work completion pattern repeats every 3 days, we can calculate the number of 3-day cycles required to complete the entire work.
Total work = W
Work completed in each 3-day cycle = 3W/10
Number of 3-day cycles required = W / (3W/10) = 10/3
Therefore, the whole work will be completed in 10/3 cycles of 3 days each.
Final Answer:
To complete the whole work, it will take 3 x (10/3) = 10 days.
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Three persons a ,b and c decide to work in such a way that a and c work together on 1st day ,b alone on 2 nd day , a and c on 3 rd and so on on alternate days .how many days will be required to complete the whole work if c and d alone finished the whole work in 20 days and 34 days respectively and b is 70% more efficient than D but 20% less efficient than A?
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