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If 5 workers can build a wall in 10 days, how long will 2 workers take?
20 days
25 days
15 days
12 days
25 days
Multiply initial workers and days to find total worker-days (5├Ч10=50), then divide by the new worker count (50/2=25).
Number of workers M1тАЛ=5, Time taken D1тАЛ=10┬аdays, New number of workers M2тАЛ=2
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Multiply initial workers and days to find total worker-days (5├Ч10=50), then divide by the new worker count (50/2=25).
Students mistakenly treat work and time as directly proportional and divide the days by the worker ratio incorrectly.
Identify the Relationship
Since fewer workers require more days to build the same wall, this is an inverse proportion problem governed by the formula M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Calculate Total Work
Find the total effort required in worker-days by multiplying the initial workers by their days: 5├Ч10=50┬аworker-days.
5├Ч10=50
Compute New Duration
Divide the total worker-days by the new number of workers to find the required time: D2тАЛ=250тАЛ=25┬аdays.
D2тАЛ=250тАЛ=25
B is correct because 2 workers will take 25 days to complete the work.
Inverse proportionality concepts appear frequently in speed-time-distance and pipes-cisterns problems in competitive exams.
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