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Paddy transplantation in Punjab is a very hard labor-intensive back-breaking job. In the transplant season, teams of special people swarm the entire rural landscape employed by the farmers and can be seen laboring away in the fields under the hot sweltering sun. Farmer Jagtar Singh has a full-time help at his sprawling farm who goes by the name of Hari, and who hails from Allahabad, UP. During the paddy transplant season, it is up to Hari to rope in his brothers, sons, and cousins from his native village to complete the task well in time. All his people are skillful and masters of the trade and equally efficient at their jobs. So, this past season, this is how the work went. Hari started the work and after 't' hours was joined in by his brother Jaggi. After another 't' hours, Neelu, their cousin, also jumped into the fray. So, after every 't' hours, 1 person kept on joining the team of already working men, and this process kept on continuing till the completion of the work. The last person worked for 't' hours. In the last season, the very same men had completed the same work working 2 shifts of 12 hours all of them working simultaneously owing to some peculiar weather conditions and time constraints. Jagtar Singh is a fair and just paymaster which is why he faces no labor shortage at this crucial time and which is why the whole 'Hari clan' are more than happy to work for him and are at his beck and call. He pays each of them individually proportional to the work done by them. This time around, Hari received 11 times as much as Surinder, his eldest son, who was the last person to join in. In how much time was the work completed?

Paddy transplantation in Punjab is a very hard labor-intensive back-breaking job. In the transplant season, teams of special people swarm the entire rural landscape employed by the farmers and can be seen laboring away in the fields under the hot sweltering sun. Farmer Jagtar Singh has a full-time help at his sprawling farm who goes by the name of Hari, and who hails from Allahabad, UP. During the paddy transplant season, it is up to Hari to rope in his brothers, sons, and cousins from his native village to complete the task well in time. All his people are skillful and masters of the trade and equally efficient at their jobs. So, this past season, this is how the work went. Hari started the work and after 't' hours was joined in by his brother Jaggi. After another 't' hours, Neelu, their cousin, also jumped into the fray. So, after every 't' hours, 1 person kept on joining the team of already working men, and this process kept on continuing till the completion of the work. The last person worked for 't' hours. In the last season, the very same men had completed the same work working 2 shifts of 12 hours all of them working simultaneously owing to some peculiar weather conditions and time constraints. Jagtar Singh is a fair and just paymaster which is why he faces no labor shortage at this crucial time and which is why the whole 'Hari clan' are more than happy to work for him and are at his beck and call. He pays each of them individually proportional to the work done by them. This time around, Hari received 11 times as much as Surinder, his eldest son, who was the last person to join in. In how much time was the work completed? Correct Answer 44 hours

Calculation:

⇒ As each of the persons is equally efficient at work, the amount each person got must have been proportional to the time each person spent working. 

⇒ As Hari got 11 times as much as Surinder and as Surinder worked for t hours, Hari must have worked for 11t hours.

⇒ The construction of the following table is useful in denoting the time spent by each person at work.

Person

Time Spent
(in hours)

1 (Hari)

11t

2 (Jaggi)

10t

3

9t

4

8t

5

7t

6

6t

7

5t

8

4t

9

3t

10

2t

11

t

Total 11

66t

 

⇒ Let the work done by 1 man in 1 hour be w.

⇒ Like last season, working together the 11 people took 24 hours (2 shifts of 12 hours each), the total work was 11 x 24 x w.

⇒ This time around, the total man-hours put were 66t hours.

⇒ So, 66 × t × w = 11 × 24 × w

⇒ Or, 6 × 11 × t = 11 × 24

⇒ Or, 11 × t = 11 × 4 = 44

⇒ Thus, total time is taken to complete the work = 11t hours = 44 hours

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