25 men with 10 boys can do in 6 days as much work as 21 men with 30 boys can do in 5 days. How many boys must help 40 men to do the same work in 4 days ?

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None of these

answer is A.

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Detailed Solution

Concept- Consider the amount of work completed by each man and boy in a single day; multiply the assumed quantity by the number of men and boys to obtain the total amount of work completed. Multiply this equation by the number of days to obtain the total amount of work completed. To determine the required quantity, compare the equations with one another.
Six days are needed to finish a project with 25 men and 10 boys.
The preceding sentence can be expressed in terms of x and y as follows: Let the work completed by each man be x and the work completed by each boy be y.

The same amount of work is finished in the same amount of time by 21 men and 30 boys, which may be expressed as -

Since both examples included the same amount of work, we may compare them as follows:

Furthering the equation's solution, we obtain –
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Now that we know how many boys will be needed to assist 40 men in finishing the identical task in four days, let that number be a.
Equation form of this assertion would be

.
We may equal the work completed in this case with any of the two equations since it is the same as the work completed in the two cases mentioned before.
Question Image

Therefore, 10 boys should assist 40 men in order to finish the job in 4 days.
Hence, the correct answer is option 1.

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