Acompany orders a number of bottles from a factory. the 8 machines in the factory could make all the bottles in 5 days. all the machines work at the same rate. for 2 days, only 4 machines are used to make the bottles. from the 3rd day, all 8 machines are used to make the bottles. work out the total number of days taken to make all the bottles.

We know that
8 machines in the factory could make all the bottles in 5 days
so
100%> 5 days
1 day> 100%/5> 20% with 8 machines
1 machine work at the rate> 20%/8> 2.5% per day

day 1> 4 machines are used to make the bottles> 4*2.5%---> 10%
day 2> 4 machines are used to make the bottles> 4*2.5%---> 10%
day 3>8 machines are used to make the bottles> 8*2.5%---> 20%
day 4>8 machines are used to make the bottles> 8*2.5%---> 20%
day 5>8 machines are used to make the bottles> 8*2.5%---> 20%
day 6>8 machines are used to make the bottles> 8*2.5%---> 20%
total work in 6 days=[10+10+20+20+20+20]> 100%

the answer is
6 days