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When A and B work with their original efficiencies, they together can complete the work in '16t' hours. When A and B work with 80% and 160% of their respective efficiencies, they together can complete the work in '15t' hours. If A alone can complete the work in 12 hours and C alone can complete the work in 6 hours less than that of B, then in what time A and C together will complete the work?
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When A and B work with their original efficiencies, they together can ...
Understanding the Problem
Given that A and B can complete the work in '16t' hours, we can derive their efficiencies:
- Let A's efficiency be 'a' and B's efficiency be 'b'.
- Together, they complete the work in 16t hours, hence:
(a + b) * 16t = 1 (work done)
When A and B work with modified efficiencies (80% and 160%), they complete the work in '15t' hours:
- Their new efficiencies are:
0.8a and 1.6b
(0.8a + 1.6b) * 15t = 1
Setting Up the Equations
We can simplify these two equations:
1. First Equation:
a + b = 1/(16t)
2. Second Equation:
0.8a + 1.6b = 1/(15t)
Now, substituting the value of (a + b) from the first equation into the second will help us find 'a' and 'b'.
Calculating Efficiencies
- Solving both equations leads to the efficiencies of A and B.
- Given that A alone can complete the work in 12 hours,
A's efficiency: a = 1/12
Hence, B's efficiency can be calculated as:
b = 1/(16t) - 1/12
Finding C's Efficiency
- If C completes the work in 6 hours less than B, let B's time be 'x' hours.
Then C's time = x - 6.
Using the efficiencies, we can express B's efficiency as:
b = 1/x
And C's efficiency can be derived from the relationship.
Time Taken by A and C Together
Now, to find the combined efficiency of A and C:
- A's efficiency: 1/12
- C's efficiency: 1/(x - 6)
Their combined efficiency will be:
(1/12) + (1/(x - 6))
Finally, to find the time taken by A and C together, use the formula:
Time = 1 / (A's efficiency + C's efficiency).
This will yield the required time for A and C to complete the work together.
Given that A and B can complete the work in '16t' hours, we can derive their efficiencies:
- Let A's efficiency be 'a' and B's efficiency be 'b'.
- Together, they complete the work in 16t hours, hence:
(a + b) * 16t = 1 (work done)
When A and B work with modified efficiencies (80% and 160%), they complete the work in '15t' hours:
- Their new efficiencies are:
0.8a and 1.6b
(0.8a + 1.6b) * 15t = 1
Setting Up the Equations
We can simplify these two equations:
1. First Equation:
a + b = 1/(16t)
2. Second Equation:
0.8a + 1.6b = 1/(15t)
Now, substituting the value of (a + b) from the first equation into the second will help us find 'a' and 'b'.
Calculating Efficiencies
- Solving both equations leads to the efficiencies of A and B.
- Given that A alone can complete the work in 12 hours,
A's efficiency: a = 1/12
Hence, B's efficiency can be calculated as:
b = 1/(16t) - 1/12
Finding C's Efficiency
- If C completes the work in 6 hours less than B, let B's time be 'x' hours.
Then C's time = x - 6.
Using the efficiencies, we can express B's efficiency as:
b = 1/x
And C's efficiency can be derived from the relationship.
Time Taken by A and C Together
Now, to find the combined efficiency of A and C:
- A's efficiency: 1/12
- C's efficiency: 1/(x - 6)
Their combined efficiency will be:
(1/12) + (1/(x - 6))
Finally, to find the time taken by A and C together, use the formula:
Time = 1 / (A's efficiency + C's efficiency).
This will yield the required time for A and C to complete the work together.
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When A and B work with their original efficiencies, they together can complete the work in '16t' hours. When A and B work with 80% and 160% of their respective efficiencies, they together can complete the work in '15t' hours. If A alone can complete the work in 12 hours and C alone can complete the work in 6 hours less than that of B, then in what time A and C together will complete the work?
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When A and B work with their original efficiencies, they together can complete the work in '16t' hours. When A and B work with 80% and 160% of their respective efficiencies, they together can complete the work in '15t' hours. If A alone can complete the work in 12 hours and C alone can complete the work in 6 hours less than that of B, then in what time A and C together will complete the work? for Bank Exams 2024 is part of Bank Exams preparation. The Question and answers have been prepared according to the Bank Exams exam syllabus. Information about When A and B work with their original efficiencies, they together can complete the work in '16t' hours. When A and B work with 80% and 160% of their respective efficiencies, they together can complete the work in '15t' hours. If A alone can complete the work in 12 hours and C alone can complete the work in 6 hours less than that of B, then in what time A and C together will complete the work? covers all topics & solutions for Bank Exams 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When A and B work with their original efficiencies, they together can complete the work in '16t' hours. When A and B work with 80% and 160% of their respective efficiencies, they together can complete the work in '15t' hours. If A alone can complete the work in 12 hours and C alone can complete the work in 6 hours less than that of B, then in what time A and C together will complete the work?.
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