certain number of people are working on constructing the room in 32 days. they worked together for 8 days and then 20% people left. 16 days after 20% people left the job, it was decided to increase the number of people to complete the work on time. find the ratio of number of new people recruited to the original number of people on the job.
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Step-by-step explanation:
Let there be n workers
Work done by each man per day = 1/32n
Amount of work done in 8 days = 8/32 = 1/4
Now workers left = n - 20%n = 4n/5
Work done by 4n/5 workers in 16 days = 4n/5 × 1/32n × 16 = 2/5
total work left = 1 - 1/4 - 2/5 = 7/20
Number of days left = 32-8-16 = 8 days
So work done per day = 7/20 ÷ 8 = 7/160
number of workers required =7/160 ÷ 1/32n = 7n/5
ratio = 7n/5 : n = 7:5
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