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Two persons could fit new windows in a house in 3 days. One of the persons fell ill before the work started. How long would the job take now?
- a)4 days
- b)8 days
- c)6 days
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Two persons could fit new windows in a house in 3 days. One of the per...
Table is in the attachment(i) Let the number of da
ys required by 1 man to fit all the windows be x.Less the number of persons, more will be the number of
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Two persons could fit new windows in a house in 3 days. One of the per...
Explanation:
To solve this problem, we need to determine the rate at which one person can fit new windows in a house and then calculate how long it would take for that person to complete the job alone.
Let's assume that the work rate of one person is represented by the variable "x" (i.e., x windows per day). Since two persons can complete the job in 3 days, the combined work rate of both persons would be 2x.
Step 1: Determine the combined work rate
- We know that the combined work rate of both persons is 2x windows per day.
- Since the work rate is measured in windows per day, we can set up the equation 2x = 1 job (since the job is to fit new windows in a house).
Step 2: Determine the work rate of one person
- To find the work rate of one person, we need to divide the combined work rate by the number of persons.
- Since one person fell ill and couldn't work, the number of persons remaining is 1.
- Therefore, the work rate of one person is (2x/2) = x windows per day.
Step 3: Determine the time required for one person to complete the job
- We know that the work rate of one person is x windows per day.
- To find the time required for one person to complete the job, we need to divide the total number of windows in the job by the work rate of one person.
- Since the total number of windows in the job is 1 and the work rate of one person is x windows per day, the time required for one person to complete the job is 1/x days.
Therefore, the job would take 1/x days for one person to complete.
Step 4: Substitute the value of x
- We determined earlier that the work rate of one person is x windows per day.
- Since we don't have any specific information about the value of x, we cannot determine the exact time required for one person to complete the job.
- However, we can conclude that the job would take longer than 3 days because if it could be completed in 3 days, the second person wouldn't have been needed in the first place.
Therefore, the correct answer is option C) 6 days, as it is the closest option to the estimated time required for one person to complete the job.
To solve this problem, we need to determine the rate at which one person can fit new windows in a house and then calculate how long it would take for that person to complete the job alone.
Let's assume that the work rate of one person is represented by the variable "x" (i.e., x windows per day). Since two persons can complete the job in 3 days, the combined work rate of both persons would be 2x.
Step 1: Determine the combined work rate
- We know that the combined work rate of both persons is 2x windows per day.
- Since the work rate is measured in windows per day, we can set up the equation 2x = 1 job (since the job is to fit new windows in a house).
Step 2: Determine the work rate of one person
- To find the work rate of one person, we need to divide the combined work rate by the number of persons.
- Since one person fell ill and couldn't work, the number of persons remaining is 1.
- Therefore, the work rate of one person is (2x/2) = x windows per day.
Step 3: Determine the time required for one person to complete the job
- We know that the work rate of one person is x windows per day.
- To find the time required for one person to complete the job, we need to divide the total number of windows in the job by the work rate of one person.
- Since the total number of windows in the job is 1 and the work rate of one person is x windows per day, the time required for one person to complete the job is 1/x days.
Therefore, the job would take 1/x days for one person to complete.
Step 4: Substitute the value of x
- We determined earlier that the work rate of one person is x windows per day.
- Since we don't have any specific information about the value of x, we cannot determine the exact time required for one person to complete the job.
- However, we can conclude that the job would take longer than 3 days because if it could be completed in 3 days, the second person wouldn't have been needed in the first place.
Therefore, the correct answer is option C) 6 days, as it is the closest option to the estimated time required for one person to complete the job.
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Two persons could fit new windows in a house in 3 days. One of the persons fell ill before the work started. How long would the job take now?a)4 daysb)8 daysc)6 daysd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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