20 workers start working on a project of packing consignments and need exactly 5 hours to pack one consignment....

Question

In a factory, 20 workers start working on a project of packing consignments. They need exactly 5 hours to pack one consignment. Every hour 4 new workers join the existing workforce. It is mandatory to relieve a worker after 10 hours. Then how many number of consignments that would be packed in the initial 113 hours?

Answer 1

20 workers ==> 1 consignment in 5 hours
1 worker ==> 1 consignment in 100 hours
4 workers ==> 1 consignment in 25 hours
Consignments done as a function of h (hours) can be written based on the above facts as shown
Consignments = (1/5)h + (1/25)(h - 1)h/2 - (1/100)×((h - 10) + (h - 20) +(h - 30) + ...... + (h - 110))
After substituting h = 113 we get Consignments approximately = 270.

Comments

Can you please elaborate how you found No. of consignements as a function of hours??

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At the begining, 20 workers are working at the speed of (1/5) consignments per hour
Now every hour 4 workers are joining and the increase in consignments produced equals
(1/25)*(1 + 2 + 3 + 4 + 5 + 6 + ........112) {for h =113}
ie., (1/25)*(1 + 2 + 3 + 4 + 5 + 6 + ........112) = (1/25)*(112*113/2)     {h*(h-1)/2}

Then there are workers that are leaving at the rate of 1 per 10 hours.
To compensate for this loss in consignments produced we need to calculate it

= (1/100)*((h-10) + (h - 20) + (h - 30) + ............ (h - (h - (h*mod*10)))).