8. 50 men can do a job working 10 hr per day in 8 days. If 20 boys and 15 girls work 15 hr per day, in how many days can the job be completed? Given that boys and girls work equally hard and each of them work half as efficiently as a man.
Answers
50 men takes 10 hours per day for 8 days to complete the job.
50 men : 8 days : 10 hours per day
Find the number of days needed if the 50 men worked 1 hour a day
10 hours a day = 8 days
1 hour a day = 8 x 10 = 80 days
Find the number of days needed if the 50 men worked 15 hour a day
1 hour = 80 days
15 hours = 80 ÷ 15 = 16/3 days
Find the number of days needed if the 1 men worked 15 hour a day
50 men = 16/3 days
1 man = 16/3 x 50 = 800/3 days
Find the number of days needed if 1 child worked 15 hours a day
Given that each child work half as efficiency as the man
1 child = 800/3 x 2 = 1600/3 days
Find the number of children working:
Total number of children = 20 boys + 15 girls = 35 children
Find the number of days needed for the 35 children to complete the work:
1 child = 1600/3
35 children = 1600/3 ÷ 35 = 15 5/21 days
Answer: The job can be completed in 15 5/21 days
= 8 days ( work finished )
.
if they work,
1 hour per day = 10 × 8 = 80 days
.
if 50 men work 15 hours per day ,
.
the work will finish in ( 80 ÷ 15 )
= 16/ 3 days
.
if 1 man work 15 hours per day then he can finish the work in
50 × 16/ 3 = 800/ 3 days
.
20 boys and 15 girls worked 15 hours per day .
since ,their efficiency is same . so then
.
total boys and girls = 20 + 15 = 35
.
efficiency of man = 2 × efficiency of each boys and girls
.
1 men can finish the work in = 800/ 3 days
1 boy/girl can finish the work in
= 2× 800/ 3 = 1600/ 3 days ,so then
.
35 boys and girls on working 15 hours per day
can finish the work in
= (1600/ 3) ÷ 35
.
= 1600 / ( 3 × 35 ) = 1600 ÷ 105
= 15 5/21 days
.
Answer :
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the work will be completed in
15 5/ 21days
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