if 50 men can do a piece of work in 12 days working 8 hours a day, how many hours a day would 60 men have to work in order to do another piece of work twice as great in 16 days?
Answers
work done in a day by 50 man = 1/12
by 60 man =1/12*6/5
=1/10
in 16 days =1/10*16
=8/5 work in 8 hour
so time required will be 10 as 8/5*10/8=10/2=2 work
50 men : 12 days : 8 hours a day
To do another work twice as work
⇒ we need twice the amount of time
⇒ 50 men : 12 x 2 days : 8 hours a day
⇒ 50 men : 24 days : 8 hours a day
Find the amount of days needed for 1 men:
50 men : 24 days : 8 hours a day
1 man : 24 x 50 days : 8 hours a day
1 man : 1200 days : 8 hours a day
Find the amount of days needed for 60 men:
60 men : 1200 ÷ 60 : 8 hours a day
60 men : 20 days : 8 hours a day
Find the number of hours needed to complete in 1 days:
60 men : 20 days : 8 hours a day
60 men : 1 days : 8 x 20 hours a day
60 men : 1 days : 160 hours a day
Find the number of hours needed to complete in 16 days:
60 men : 1 days : 160 hours a day
60 men : 16 days : 160 ÷ 16 hours a day
60 men : 16 days : 10 hours a day
Answer: the 60 men will need to work 10 hours a day for 16 days.
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ALTERNATIVE METHOD:
50 men = 12 days (Given)
To do a work twice as great:
50 men = 12 x 2 = 24 days
To do the work with 60 men:
50 men = 24 days
1 man = 24 x 50 = 1200 days
60 men = 1200 ÷ 60 = 20 days
To do the with 16 days
20 days = 8 hours a day
1 day = 8 x 20 = 160 hours a day
16 days = 160 ÷ 16 = 10 hours a day
Answer: 10 hours a day