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A can do a certain work in the same time in which B and C together can do it. If A and B could together do it in 10 days and C alone in 50 days, then B alone could do it in
- a)15 days
- b)20 days
- c)25 days
- d)30 days
Correct answer is option 'C'. Can you explain this answer?
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A can do a certain work in the same time in which B and C together can...
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A can do a certain work in the same time in which B and C together can...
Given information:
- A can do the work in the same time as B and C together.
- A and B together can do the work in 10 days.
- C alone can do the work in 50 days.
Calculating work efficiency:
Let's assume that A can do 1 unit of work in x days. Therefore, B can do 1 unit of work in y days and C can do 1 unit of work in z days.
Using the given information, we can calculate the work efficiency of each person:
- A completes 1 unit of work in x days, so A's efficiency is 1/x units of work per day.
- B completes 1 unit of work in y days, so B's efficiency is 1/y units of work per day.
- C completes 1 unit of work in z days, so C's efficiency is 1/z units of work per day.
Equations:
According to the given information, we know that:
- A and B together can complete the work in 10 days, so their combined efficiency is 1/10 units of work per day.
- A can do the work in the same time as B and C together, so their combined efficiency is 1/x units of work per day.
Solving the equations:
We can set up the following equations based on the given information:
1) A + B = 1/10 (Equation 1)
2) A = 1/x (Equation 2)
3) A + B + C = 1/x (Equation 3)
4) C = 1/50 (Equation 4)
Using Equations 2 and 3, we can substitute the value of A from Equation 2 into Equation 3:
1/x + B + C = 1/x
Simplifying the equation, we get:
B + C = 0
This implies that B and C together can do 0 units of work per day. Since C can do 1 unit of work in 50 days (Equation 4), B must be able to do the remaining work on its own.
Calculating B's work efficiency:
Since B can do the remaining work on its own, B's efficiency is 1 unit of work in b days.
Therefore, B can do the work in 50 days, which corresponds to option C.
- A can do the work in the same time as B and C together.
- A and B together can do the work in 10 days.
- C alone can do the work in 50 days.
Calculating work efficiency:
Let's assume that A can do 1 unit of work in x days. Therefore, B can do 1 unit of work in y days and C can do 1 unit of work in z days.
Using the given information, we can calculate the work efficiency of each person:
- A completes 1 unit of work in x days, so A's efficiency is 1/x units of work per day.
- B completes 1 unit of work in y days, so B's efficiency is 1/y units of work per day.
- C completes 1 unit of work in z days, so C's efficiency is 1/z units of work per day.
Equations:
According to the given information, we know that:
- A and B together can complete the work in 10 days, so their combined efficiency is 1/10 units of work per day.
- A can do the work in the same time as B and C together, so their combined efficiency is 1/x units of work per day.
Solving the equations:
We can set up the following equations based on the given information:
1) A + B = 1/10 (Equation 1)
2) A = 1/x (Equation 2)
3) A + B + C = 1/x (Equation 3)
4) C = 1/50 (Equation 4)
Using Equations 2 and 3, we can substitute the value of A from Equation 2 into Equation 3:
1/x + B + C = 1/x
Simplifying the equation, we get:
B + C = 0
This implies that B and C together can do 0 units of work per day. Since C can do 1 unit of work in 50 days (Equation 4), B must be able to do the remaining work on its own.
Calculating B's work efficiency:
Since B can do the remaining work on its own, B's efficiency is 1 unit of work in b days.
Therefore, B can do the work in 50 days, which corresponds to option C.
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Community Answer
A can do a certain work in the same time in which B and C together can...
Let, B alone completes the work in x days.
ATP, 10*[(1/x) + (1/x + 1/50)] = 1 ... => 20/x = 4/5 ... => x = 25
Hence, B alone completes the work in 25 days.
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A can do a certain work in the same time in which B and C together can do it. If A and B could together do it in 10 days and C alone in 50 days, then B alone could do it ina)15 daysb)20 daysc)25 daysd)30 daysCorrect answer is option 'C'. Can you explain this answer?
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