It takes 30 days when 8 men construct a flat. How many men is needed to construct the same flat in 20 days if they work at the same rate?
To solve this problem, we can use the formula:
(work rate) = (number of workers) / (number of days)
Let's denote the number of workers needed to construct the flat in 20 days as x.
For the first scenario, we have:
(work rate) = 8 / 30
For the second scenario, we have:
(work rate) = x / 20
Since the work rate is the same in both scenarios (as stated in the problem), we can equate the two equations and solve for x:
8 / 30 = x / 20
Cross multiplying:
x = (8 / 30) * 20
Simplifying:
x = 16/3
So, approximately 5.33 men are needed to construct the same flat in 20 days. Since we cannot have fractional workers, we would round up to the nearest whole number. Therefore, it would require 6 men to construct the flat in 20 days at the same work rate.
To determine the number of men needed to construct the same flat in 20 days, we can use the formula:
(M1 * D1 * T1) = (M2 * D2 * T2)
Where:
M1 and M2 are the number of men in the first and second scenarios, respectively.
D1 and D2 are the number of days in the first and second scenarios, respectively.
T1 and T2 are the time taken in the first and second scenarios, respectively.
Given that:
M1 = 8 (number of men in the first scenario)
D1 = 30 (number of days in the first scenario)
T1 = 1 (work rate of the men in the first scenario; they complete 1 flat in 30 days)
D2 = 20 (number of days in the second scenario)
T2 = 1 (work rate of the men in the second scenario; we want to find the number of men, M2)
Plugging in the values, we get:
(8 * 30 * 1) = (M2 * 20 * 1)
240 = 20M2
M2 = 240 / 20
M2 = 12
Therefore, to construct the same flat in 20 days, 12 men are needed.