24 men working 8 h a day can finish a work in 10 days. Working at a rate of 10 h a day, thenumber of men required to finish the work in 6 days isa)30b)32c)34d)36Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
● 24 men can finish a work in 10 days working 8 hours a day
● The goal is to finish the work in 6 days working 10 hours a day
● We need to find the number of men required to finish the work in the given time frame

Solution:
Step 1: Calculate the total work to be done
● Let's assume that the total work to be done is 'W'
● According to the given information, 24 men can finish the work in 10 days working 8 hours a day
● So, the total work done by these 24 men in 10 days = 24 x 8 x 10 = 1920 man-hours
● Therefore, we can say that the total work to be done (W) = 1920

Step 2: Calculate the rate of work done by 24 men working 8 hours a day
● Rate of work = Total work done / Total time taken
● Rate of work done by 24 men working 8 hours a day = 1920 / (24 x 8 x 10) = 1/4

Step 3: Calculate the number of men required to finish the work in 6 days working 10 hours a day
● Let's assume that the required number of men is 'x'
● According to the given information, we need to finish the work in 6 days working 10 hours a day
● So, the total time taken to finish the work = 6 x 10 = 60 hours
● Therefore, the rate of work required to finish the work in the given time frame = Total work to be done / Total time taken = W / 60
●The rate of work done by one man working 10 hours a day = (1/4) x (8/10) = 1/5
●Therefore, the required number of men = (W / 60) / (1/5) = (1920 / 60) x 5 = 32

Hence, the correct answer is option B (32).

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