Had Ajinkya not planted any tree in month 5, by how much would his average change?
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NameMonth 1Month 2Month 4Month 4Month 5AverageSuresh122737475736Virat112131465633Rohit92434445433Ajinkya102035455533Mahendra152535506037Shikar213146566644
Had each of the six planted 10 trees more in a month than in the previous month for all the five months, their averages would be:
Suresh: 32, Virat: 31, Rohit: 29, Ajinkya: 30, Mahendra: 35, Shikhar: 41.
But the actual averages are: Suresh: 36, Virat: 33, Rohit: 33, Ajinkya: 33, Mahendra: 37, Shikhar: 44.
Since there is a difference of 4 between the expected average and actual average, Suresh planted 4 × 5 = 20 more trees than expected. Similarly, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 10, 20, 15, 10 and 15 more trees respectively than expected.
Now If any of these people had planted 15 trees more than the previous month in month 5, then the number of excess trees planted would only have been 5. Similarly, had the person planted 15 trees more than the previous month in month 4, the number of excess trees planted would be 5 + 5 = 10. Thus, if a person planted 15 trees more than the previous month in month 2, month 3, month 4 or month 5, the corresponding number of total excess trees would be 20, 15, 10 and 5 respectively. Thus, Suresh, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 15 more trees than the previous month in month 2, month 4, month 2, month 3, month 4 and month 3 respectively.
Thus, the number of trees planted by them in each month can be calculated as shown in the table above.
Thus, Suresh planted 47 trees in month 4.
Alternatively,
From month 2 onwards, each person plants 10 more trees in every subsequent month and 15 more trees than the previous month in exactly one month. If the person plants x trees in month 1 and had planted exactly 10 more trees in each subsequent month, the total number of trees planted by that person would be x + (x+ 10) + (x+ 20) + (x+ 30) + (x+ 40) = 5x+ 100.
Now, if the person had planted 15 trees more than the previous month in month 2, the total number of trees would be x + (x+ 15) + (x+ 25) + (x+ 35) + (x+ 45) = 5x+ 100 + (5 × 4). On the other hand, if the person had planted 15 trees more than the previous month in month 5, the total number of trees would be x+ (x+ 10) + (x+ 20) + (x+ 30) + (x+ 45) = 5x+ 100 + (5 × 1). Thus, if a person had planted 15 more trees than the previous month in month, the total number of trees planted by that person = 5x+ 100 + (5 × No. of months to go from month of planting to end of tenure (p)).
Total number of trees planted by Suresh = 36 × 5 = 180
∴(5 × 12) + 100 + 5p= 180 ⇒p= 4
This simply means that Suresh planted 15 more trees than the previous month in month 4.
Using this approach, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 15 more trees than the previous month in month 4, month 2, month 3, month 4 and month 3 respectively.
Thus, Suresh planted 47 trees in month 4.
If Ajinkya did not plant 55 trees in month 5, the total number of trees planted by him would drop by 55 and his average would change by 55/5 = 11.
Note:Even if Ajinkya does not plant any trees in a month, his average would still be calculated for all the five months, and not just for the number of months in which he planted trees.
NameMonth 1Month 2Month 4Month 4Month 5AverageSuresh122737475736Virat112131465633Rohit92434445433Ajinkya102035455533Mahendra152535506037Shikar213146566644
Had each of the six planted 10 trees more in a month than in the previous month for all the five months, their averages would be:
Suresh: 32, Virat: 31, Rohit: 29, Ajinkya: 30, Mahendra: 35, Shikhar: 41.
But the actual averages are: Suresh: 36, Virat: 33, Rohit: 33, Ajinkya: 33, Mahendra: 37, Shikhar: 44.
Since there is a difference of 4 between the expected average and actual average, Suresh planted 4 × 5 = 20 more trees than expected. Similarly, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 10, 20, 15, 10 and 15 more trees respectively than expected.
Now If any of these people had planted 15 trees more than the previous month in month 5, then the number of excess trees planted would only have been 5. Similarly, had the person planted 15 trees more than the previous month in month 4, the number of excess trees planted would be 5 + 5 = 10. Thus, if a person planted 15 trees more than the previous month in month 2, month 3, month 4 or month 5, the corresponding number of total excess trees would be 20, 15, 10 and 5 respectively. Thus, Suresh, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 15 more trees than the previous month in month 2, month 4, month 2, month 3, month 4 and month 3 respectively.
Thus, the number of trees planted by them in each month can be calculated as shown in the table above.
Thus, Suresh planted 47 trees in month 4.
Alternatively,
From month 2 onwards, each person plants 10 more trees in every subsequent month and 15 more trees than the previous month in exactly one month. If the person plants x trees in month 1 and had planted exactly 10 more trees in each subsequent month, the total number of trees planted by that person would be x + (x+ 10) + (x+ 20) + (x+ 30) + (x+ 40) = 5x+ 100.
Now, if the person had planted 15 trees more than the previous month in month 2, the total number of trees would be x + (x+ 15) + (x+ 25) + (x+ 35) + (x+ 45) = 5x+ 100 + (5 × 4). On the other hand, if the person had planted 15 trees more than the previous month in month 5, the total number of trees would be x+ (x+ 10) + (x+ 20) + (x+ 30) + (x+ 45) = 5x+ 100 + (5 × 1). Thus, if a person had planted 15 more trees than the previous month in month, the total number of trees planted by that person = 5x+ 100 + (5 × No. of months to go from month of planting to end of tenure (p)).
Total number of trees planted by Suresh = 36 × 5 = 180
∴(5 × 12) + 100 + 5p= 180 ⇒p= 4
This simply means that Suresh planted 15 more trees than the previous month in month 4.
Using this approach, Virat, Rohit, Ajinkya, Mahendra and Shikhar planted 15 more trees than the previous month in month 4, month 2, month 3, month 4 and month 3 respectively.
Thus, Suresh planted 47 trees in month 4.
If Ajinkya did not plant 55 trees in month 5, the total number of trees planted by him would drop by 55 and his average would change by 55/5 = 11.
Note:Even if Ajinkya does not plant any trees in a month, his average would still be calculated for all the five months, and not just for the number of months in which he planted trees.
