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Anup can dig a well in 10 days. but particularly in difficult time the work is such that due to fatigue every subsequent day efficiency of a worker falls by 10%.If Anup is given a task of digging one such well in the difficult time, then in how many days will he finish the work?
- a)12th day
- b)15 th day
- c)11th day
- d)Never
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Anup can dig a well in 10 days. but particularly in difficult time the...
Correct Answer :- d
Explanation : The total no. of days in which Anoop can dig the well is 10 days.
Anoop's one day efficiency is 10%.
On day one Anoop performs 10% of his work efficiency, then the next day he won't be able to perform because as per the question the efficiency of a worker falls by 10%.
thus, 10%-10% = 0.
Most Upvoted Answer
Anup can dig a well in 10 days. but particularly in difficult time the...
Let us assume that digging one well = 40 unit
Efficiency of Anup = 40/10 = 4 unit/day
Now efficiency is falling by 10%
So, this is case of GP
⇒ 4,18/5,81/25,…… where common ratio = 9/10
Now, sum of infinite GP = a / (1 – r)
⇒ 4/ (1 – 9/10) = 40
Hence, it is clear that Anup will takes infinite time, so he will never finish the work.
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Community Answer
Anup can dig a well in 10 days. but particularly in difficult time the...
Efficiency of Workers
Anoop and Sandeep have different efficiencies when it comes to digging a well. Anoop can dig a well in 10 days while Sandeep can dig a well in 5 days.
Fatigue and Reduced Efficiency
However, due to the difficult terrain, the efficiency of a worker falls by 10% every subsequent day. This means that the amount of work that Anoop can do in a day decreases by 10% for every day that he works on the well.
Calculating the Time Taken
To calculate the time taken by Anoop to dig a well in the difficult terrain, we need to take into account his reduced efficiency. Let's assume that the well is of a size that would normally take Anoop 10 days to dig. On the first day, Anoop will be able to work at his normal efficiency and complete 1/10th of the work.
On the second day, his efficiency will fall by 10%, which means that he will only be able to complete 90% of the work that he would normally be able to do. This means that on the second day, he will only be able to complete 9/100th of the work.
Similarly, on the third day, his efficiency will fall by another 10%, which means that he will only be able to complete 81% of the work that he would normally be able to do. This means that on the third day, he will only be able to complete 81/1000th of the work.
Continuing in this way, we can see that Anoop will never be able to complete the well. This is because his efficiency falls so quickly that he will not be able to complete even a small amount of work each day.
Therefore, the correct answer is option 'D' - never.
Anoop and Sandeep have different efficiencies when it comes to digging a well. Anoop can dig a well in 10 days while Sandeep can dig a well in 5 days.
Fatigue and Reduced Efficiency
However, due to the difficult terrain, the efficiency of a worker falls by 10% every subsequent day. This means that the amount of work that Anoop can do in a day decreases by 10% for every day that he works on the well.
Calculating the Time Taken
To calculate the time taken by Anoop to dig a well in the difficult terrain, we need to take into account his reduced efficiency. Let's assume that the well is of a size that would normally take Anoop 10 days to dig. On the first day, Anoop will be able to work at his normal efficiency and complete 1/10th of the work.
On the second day, his efficiency will fall by 10%, which means that he will only be able to complete 90% of the work that he would normally be able to do. This means that on the second day, he will only be able to complete 9/100th of the work.
Similarly, on the third day, his efficiency will fall by another 10%, which means that he will only be able to complete 81% of the work that he would normally be able to do. This means that on the third day, he will only be able to complete 81/1000th of the work.
Continuing in this way, we can see that Anoop will never be able to complete the well. This is because his efficiency falls so quickly that he will not be able to complete even a small amount of work each day.
Therefore, the correct answer is option 'D' - never.
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