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Q. A piece of work can be done by 8 men or 12 boys in 20 days.How long will it be taken by 6 men and 6 boys to complete the work?
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Given :
8 men can complete the piece of work in 20 days.
=> 1 man can complete the work in 20 X 8 days => 160 days.
=> In one day, one man can complete 1/160th of the work.
Similarly,
12 boys can complete the piece of work in 20 days.
=> 1 boy can complete the work in 20 X 12 days => 240 days.
=> In one day, one boy can complete 1/240th of the work.
The amount of work completed by 6 men and 6 boys in one day,
= 6*(1/60) + 6*(1/240) = 6/160 + 6/240
= 3/80 + 2/80 = [3+2]/80 = 5/80 = 1/16.
Therefore, the no. of days required to complete the work by 6 men and 6 boys working together is 16 days.
8 men can complete the piece of work in 20 days.
=> 1 man can complete the work in 20 X 8 days => 160 days.
=> In one day, one man can complete 1/160th of the work.
Similarly,
12 boys can complete the piece of work in 20 days.
=> 1 boy can complete the work in 20 X 12 days => 240 days.
=> In one day, one boy can complete 1/240th of the work.
The amount of work completed by 6 men and 6 boys in one day,
= 6*(1/60) + 6*(1/240) = 6/160 + 6/240
= 3/80 + 2/80 = [3+2]/80 = 5/80 = 1/16.
Therefore, the no. of days required to complete the work by 6 men and 6 boys working together is 16 days.
Charchil23:
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