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X can do a piece of work alone in 20 days, if he devotes 9 hours daily. However X works alone on the 1st day and on the 2nd day one man whose capacity to do the work is twice as that of X, joined in. On the 3rd day, another man whose capacity is thrice as that of X, joined and similarly on the 4th day, another man whose capacity is four times as that of X, joined them. The process continues this way until the work is completed. On which day will the work be completed, if everyone works for five hours a day?
- a)5th day
- b)6th day
- c)7th day
- d)8th day
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
X can do a piece of work alone in 20 days, if he devotes 9 hours dail...
Since X takes 20 days working 9 hours a day to complete the work, the total man - hours required to complete this work would be 180 man - hours.
Amount of work done in the 1st day by X = 5 hours = 5 man - hours
On the 2nd day, X does again 5 man - hours of work. The 2nd person being twice as efficient as X, will do double the work that X does, which is 10 man - hours of work.
Total work done on 2nd day = 5 + 10 = 15 man - hours
3rd day, X does 5 man - hours of work. 2nd person does 10 man - hours of work. 3rd person who is thrice as efficient as X does 15 man - hours of work.
Total work done on 3rd day = 5 + 10 + 15 = 30 man - hours
Similarly on 4th day the amount of work done would be = 5 + 10 + 15 + 20 = 50 man - hours
Similarly on 5th day the amount of work done would be = 5 + 10 + 15 + 20 + 25 = 75 man - hours
Total work done after 5 days = 5 + 15 + 30 + 50 + 75 = 175 man - hours.
On the 6th day the work remaining will be 5 man - hours.
But on the 6th day the amount of work that can be done is = 5 + 10 + 15 +20 + 25 + 30 = 105 man - hours.
Thus we can see that the work will be complete on the 6th day itself.
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Community Answer
X can do a piece of work alone in 20 days, if he devotes 9 hours dail...
To solve this problem, let's break it down into individual steps and calculate the work done by each person on each day.
Step 1: Calculate X's work rate per hour
X can complete the work alone in 20 days, devoting 9 hours daily. So, X's work rate per day is 1/20 and his work rate per hour is 1/20 divided by 9, which is 1/180.
Step 2: Calculate the work rate of each additional person
The second person's capacity is twice that of X, so his work rate per hour is 2 times X's work rate per hour, which is 2/180 or 1/90.
The third person's capacity is three times that of X, so his work rate per hour is 3 times X's work rate per hour, which is 3/180 or 1/60.
The fourth person's capacity is four times that of X, so his work rate per hour is 4 times X's work rate per hour, which is 4/180 or 1/45.
Step 3: Calculate the total work rate per hour
To calculate the total work rate per hour, we add up the work rates of all the people working on a particular day. On the first day, only X is working, so the total work rate per hour is 1/180.
On the second day, X and the second person are working. So the total work rate per hour is 1/180 + 1/90 = 3/180 = 1/60.
On the third day, X, the second person, and the third person are working. So the total work rate per hour is 1/180 + 1/90 + 1/60 = 9/180 = 1/20.
On the fourth day, X, the second person, the third person, and the fourth person are working. So the total work rate per hour is 1/180 + 1/90 + 1/60 + 1/45 = 19/180.
Step 4: Calculate the time taken to complete the work
Since we now know the total work rate per hour, we can calculate the time taken to complete the work by dividing the total work required by the total work rate per hour.
If everyone works for 5 hours a day, the total work done in a day is the total work rate per hour multiplied by 5.
On the first day, the work done is (1/180) * 5 = 1/36.
On the second day, the work done is (1/60) * 5 = 1/12.
On the third day, the work done is (1/20) * 5 = 1/4.
On the fourth day, the work done is (19/180) * 5 = 19/36.
We can observe that the work done is increasing each day. So, the work will be completed on the 6th day when the work done is 1 (the total work required).
Therefore, the correct answer is option (b) 6th day.
Step 1: Calculate X's work rate per hour
X can complete the work alone in 20 days, devoting 9 hours daily. So, X's work rate per day is 1/20 and his work rate per hour is 1/20 divided by 9, which is 1/180.
Step 2: Calculate the work rate of each additional person
The second person's capacity is twice that of X, so his work rate per hour is 2 times X's work rate per hour, which is 2/180 or 1/90.
The third person's capacity is three times that of X, so his work rate per hour is 3 times X's work rate per hour, which is 3/180 or 1/60.
The fourth person's capacity is four times that of X, so his work rate per hour is 4 times X's work rate per hour, which is 4/180 or 1/45.
Step 3: Calculate the total work rate per hour
To calculate the total work rate per hour, we add up the work rates of all the people working on a particular day. On the first day, only X is working, so the total work rate per hour is 1/180.
On the second day, X and the second person are working. So the total work rate per hour is 1/180 + 1/90 = 3/180 = 1/60.
On the third day, X, the second person, and the third person are working. So the total work rate per hour is 1/180 + 1/90 + 1/60 = 9/180 = 1/20.
On the fourth day, X, the second person, the third person, and the fourth person are working. So the total work rate per hour is 1/180 + 1/90 + 1/60 + 1/45 = 19/180.
Step 4: Calculate the time taken to complete the work
Since we now know the total work rate per hour, we can calculate the time taken to complete the work by dividing the total work required by the total work rate per hour.
If everyone works for 5 hours a day, the total work done in a day is the total work rate per hour multiplied by 5.
On the first day, the work done is (1/180) * 5 = 1/36.
On the second day, the work done is (1/60) * 5 = 1/12.
On the third day, the work done is (1/20) * 5 = 1/4.
On the fourth day, the work done is (19/180) * 5 = 19/36.
We can observe that the work done is increasing each day. So, the work will be completed on the 6th day when the work done is 1 (the total work required).
Therefore, the correct answer is option (b) 6th day.
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X can do a piece of work alone in 20 days, if he devotes 9 hours daily. However X works alone on the 1st day and on the 2nd day one man whose capacity to do the work is twice as that of X, joined in. On the 3rd day, another man whose capacity is thrice as that of X, joined and similarly on the 4th day, another man whose capacity is four times as that of X, joined them. The process continues this way until the work is completed. On which day will the work be completed, if everyone works for five hours a day?a)5th dayb)6th dayc)7th dayd)8th dayCorrect answer is option 'B'. Can you explain this answer?
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