Question

$30$ persons can reap a field in $17$ days. How many more persons should be engaged to reap the same field in $10$ days?

Answer 1

Hint: This is a work – time (sometimes called work – men problem) word problem. For solving this question, if there are less persons working, the time to be taken to complete the work will be more as compared to the condition of there are more persons working.

Complete step-by-step answer:
We are given that a field can be reaped by $30$ person in $17$ days. We need to find out the number of persons required for completing the reaping of the same field in $10$ days.
According to our intuition, more the number of the persons reaping the field, lesser is the number of days required and lesser the number of persons reaping the field, more is the number of days required. Hence, the number of persons required to complete the reaping of the field in $10$ days will be more than $30$ persons. The number of persons is inversely proportional to the number of days in which the field will be reaped. The only thing that remains constant is the amount of work, in this case the reaping of the field. Work done by people is given by: Number of person times the number of days. Let the number of persons required to complete the reaping of the field in $10$ days be $x$ . Therefore:
$17\times 30=10\times x$
$\Rightarrow x=51$
Hence, the number of people required for completing the reaping of the field in $10$ days are $51$ .

Note: We make a very common mistake without thinking that more the number of people, more will be the number of days. This is a very common mistake and a very silly mistake.