Let x represent the amount of work that can be done by a man, and let y represent the amount of work that can be done by a boy. Then and . Solve these two equations simultaneously for x and y, then use this to answer the remainder of your question.
2 men and 7 boys can do a piece of work in 14 days,
3 men and 8 boys can do it in 11 days.
8 men and 6 boys can do this 3 times of work in how many days?
Logic: I found either the first or the second sentence is redundant, but when I ignored one and tried solving, it gives me wrong answers, Kindly help how to approach?
Let x represent the amount of work that can be done by a man, and let y represent the amount of work that can be done by a boy. Then and . Solve these two equations simultaneously for x and y, then use this to answer the remainder of your question.
Hello, hisajesh!
I assume that all the men work at the same constant rate
and that all the boys work at the same constant rate.
2 men and 7 boys can do a piece of work in 14 days,
3 men and 8 boys can do it in 11 days.
8 men and 6 boys can do this 3 times of work in how many days?
Let = the number of days it takes one man to do the job..
In one day, a man can do of the job.
In one day, 2 men can do of the job.
Let = the number of days it takes one boy to do the job.
In one day, a boy can do of the job.
In one day, 7 boys can do of the job.
So, in one day, 2 men and 7 boys can do of the job.
. . But this equals of the job.
Hence: .
In one day, 3 men can do of the job.
In one day, 8 boys can do of the job.
So in one day, 3 men and 8 boys can do of the job.
. . But this equals of the job.
Hence: .
We have a system of equations: .
Add: .
Substitute into [1]: .
Now we know the following:
In one day, a man can do of the jpb.
In one day, 8 men can do of the job.
In days, 8 men can do of the job.
In one day, a boy can do of the job.
In one day, 6 boys can do of the job.
In days, 6 boys can do of the job.
In days, 8 men and 6 boys can do: of the job.
But this equals 3 jobs.
Hence: .
Multiply by 77: .
Answer: 21 days.