Answer:
Easy
Explanation:
Let the time taken by Badri to complete the work be B. Then Amit can complete the work in 2.25 days, so we can write:
A = 2.25/B
Chetan takes double that of Badri to complete the work, so we can write:
C = 2B
Das takes double that of Chetan to complete the work, so we can write:
D = 2C = 4B
Let the first group consist of Amit and Das, and the second group consist of Badri and Chetan. Then the time taken by the first group to complete the work is:
T1 = A + D = 2.25/B + 4B
The time taken by the second group to complete the work is:
T2 = B + C = B + 2B = 3B
The difference between the times taken by the two groups to complete the work is:
T2 - T1 = 3B - (2.25/B + 4B) = 3B - 2.25/B - 4B
To minimize this difference, we take the derivative with respect to B and set it equal to zero:
d/dB (3B - 2.25/B - 4B) = 0
3 + 2.25/B^2 - 4 = 0
2.25/B^2 = 1
B = sqrt(2.25) = 1.5
Therefore, the time taken by Badri to complete the work is B = 1.5 days. Amit takes 2.25/1.5 = 1.5 days, Chetan takes 2B = 3 days, and Das takes 4B = 6 days.
To minimize the difference between the times taken by the two groups, we can take the faster group to consist of Amit and Badri, and the slower group to consist of Chetan and Das. The faster group takes 1.5 + 1.5 = 3 days to complete the work, and the slower group takes 3 + 6 = 9 days to complete the work. Therefore, the composition of the faster group could be Amit and Badri.