DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > Working alone at their respective constant ra...
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?
- a)46/9
- b)50/9
- c)50/11
- d)36/7
- e)210/41
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Working alone at their respective constant rates, A can complete a tas...
Given:
A can complete the task in 'a' days
B can complete the task in 'b' days
Approach:
1. Let's first calculate the fraction of work done by A and B in a day.
2. Then, we will calculate the fraction of work done by A and B in 2 days.
3. Using this information, we will calculate the number of days taken when they work together.
Calculations:
Fraction of work done by A in a day:
A completes 1/a of the work in a day
Fraction of work done by B in a day:
B completes 1/b of the work in a day
Fraction of work done by A and B in 2 days:
In 2 days, A completes 2/a of the work
In 2 days, B completes 2/b of the work
Given conditions:
When A starts, they finish the task in exactly 10 days.
A works 2 days at a time, so in 10 days, A works 5 sets of 2 days.
Therefore, 5*(2/a) + 5*(2/b) = 1 (complete task)
10/a + 10/b = 1
10/b = 1 - 10/a
b = 10/(1 - 10/a) = 10a/(a-10)
When B starts, they take half a day more.
Similarly, 5*(2/b) + 5*(2/a) = 1
10/b + 10/a = 1
10/a = 1 - 10/b
a = 10/(1 - 10/b) = 10b/(b-10)
Calculating time taken when they work together:
Let x be the number of days taken when A and B work together
A completes x/2 sets of work
B completes x/2 sets of work
x/2 * (2/a + 2/b) = 1
x/2 * (a+b)/ab = 1
x = 2ab/(a+b)
Substitute the values of a and b:
x = 2(10a/(a-10))(10b/(b-10)) / (10a/(a-10) + 10b/(b-10))
x = 36/7 days
Therefore, when A and B work together, they complete the task in 36/7 days. Option D is the correct answer.
A can complete the task in 'a' days
B can complete the task in 'b' days
Approach:
1. Let's first calculate the fraction of work done by A and B in a day.
2. Then, we will calculate the fraction of work done by A and B in 2 days.
3. Using this information, we will calculate the number of days taken when they work together.
Calculations:
Fraction of work done by A in a day:
A completes 1/a of the work in a day
Fraction of work done by B in a day:
B completes 1/b of the work in a day
Fraction of work done by A and B in 2 days:
In 2 days, A completes 2/a of the work
In 2 days, B completes 2/b of the work
Given conditions:
When A starts, they finish the task in exactly 10 days.
A works 2 days at a time, so in 10 days, A works 5 sets of 2 days.
Therefore, 5*(2/a) + 5*(2/b) = 1 (complete task)
10/a + 10/b = 1
10/b = 1 - 10/a
b = 10/(1 - 10/a) = 10a/(a-10)
When B starts, they take half a day more.
Similarly, 5*(2/b) + 5*(2/a) = 1
10/b + 10/a = 1
10/a = 1 - 10/b
a = 10/(1 - 10/b) = 10b/(b-10)
Calculating time taken when they work together:
Let x be the number of days taken when A and B work together
A completes x/2 sets of work
B completes x/2 sets of work
x/2 * (2/a + 2/b) = 1
x/2 * (a+b)/ab = 1
x = 2ab/(a+b)
Substitute the values of a and b:
x = 2(10a/(a-10))(10b/(b-10)) / (10a/(a-10) + 10b/(b-10))
x = 36/7 days
Therefore, when A and B work together, they complete the task in 36/7 days. Option D is the correct answer.
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Community Answer
Working alone at their respective constant rates, A can complete a tas...
Given Information:
- A completes a task in 'a' days
- B completes a task in 'b' days
- They take turns working 2 days at a time
- If A starts, they finish the task in 10 days
- If B starts, they take half a day more than when A starts
Calculating Efficiency:
- A's efficiency = 1/a (work done per day)
- B's efficiency = 1/b (work done per day)
- Together, their efficiency = 1/a + 1/b
Calculating Total Work:
- When A starts, in 10 days, A works for 6 days and B works for 4 days
- Total work = 10 * (1/a + 1/b) = 10(6/a + 4/b)
When B starts:
- B takes half a day more than A, so B works for 5 days and A works for 5 days
- Total work = 10(5/a + 5/b)
Solving for a and b:
- Equating the two total work equations:
10(6/a + 4/b) = 10(5/a + 5/b)
60/a + 40/b = 50/a + 50/b
10/a = 10/b
b = a
When A and B work together:
- Total work = 10(1/a + 1/b) = 10(2/a) = 20/a days
Substitute b = a:
Total work = 20/a days = 10(2/a) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) =
- A completes a task in 'a' days
- B completes a task in 'b' days
- They take turns working 2 days at a time
- If A starts, they finish the task in 10 days
- If B starts, they take half a day more than when A starts
Calculating Efficiency:
- A's efficiency = 1/a (work done per day)
- B's efficiency = 1/b (work done per day)
- Together, their efficiency = 1/a + 1/b
Calculating Total Work:
- When A starts, in 10 days, A works for 6 days and B works for 4 days
- Total work = 10 * (1/a + 1/b) = 10(6/a + 4/b)
When B starts:
- B takes half a day more than A, so B works for 5 days and A works for 5 days
- Total work = 10(5/a + 5/b)
Solving for a and b:
- Equating the two total work equations:
10(6/a + 4/b) = 10(5/a + 5/b)
60/a + 40/b = 50/a + 50/b
10/a = 10/b
b = a
When A and B work together:
- Total work = 10(1/a + 1/b) = 10(2/a) = 20/a days
Substitute b = a:
Total work = 20/a days = 10(2/a) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) = 10(2/5) =
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?.
Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?.
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Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Working alone at their respective constant rates, A can complete a task in ‘a’ days and B in ‘b’ days. They take turns in doing the task with each working 2 days at a time. If A starts they finish the task in exactly 10 days. If B starts, they take half a day more. How long does it take to complete the task if they both work together?a)46/9b)50/9c)50/11d)36/7e)210/41Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice DSSSB TGT/PGT/PRT tests.
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