Amit can complete a work in 'D' days while Deepak takes 'D+1' days to complete the same work. Mohit who is 40% less efficient than Deepak can complete the work with the help of Amit in 10/3 days. In how many days Amit & Deepak together can finish the work?
Answers
Answer:
Amit and Deepak together can finish the work in 7/3 days.
Step-by-step explanation:
Let's assume that Amit can complete the work in D days, so his work efficiency is 1/D. And, Deepak can complete the same work in D+1 days, so his work efficiency is 1/(D+1).
Now, Mohit is 40% less efficient than Deepak, so his work efficiency is 0.6*(1/(D+1)) = 0.6/(D+1).
Given that, Mohit can complete the work with the help of Amit in 10/3 days. So, their combined work efficiency is 1/(10/3) = 3/10.
Now, let's consider Amit and Deepak together to finish the work in x days. So, their combined work efficiency is 1/x.
According to the given condition, Amit and Mohit can finish the work in 10/3 days. So, their combined work efficiency is (1/D) + (0.6/(D+1)) = 3/10.
Similarly, the combined work efficiency of Amit and Deepak is (1/D) + (1/(D+1)) = 1/x.
Now, equating the above two equations, we get:
(1/D) + (1/(D+1)) = 1/x - 0.6/(D+1)
Simplifying the above equation, we get:
(2D+1)/(D*(D+1)) = (x-0.6)/(x*(D+1))
Cross-multiplying the above equation, we get:
x*(2D+1) = (D*(D+1)) * (x-0.6)
Expanding the above equation, we get:
2Dx + x = Dx^2 + Dx - 0.6D - 0.6
Simplifying the above equation, we get:
Dx^2 - 1.4Dx - 0.6 = 0
Using the quadratic formula, we get:
x = [1.4D ± sqrt((1.96D^2) + 2.4D)]/2D
Since x should be greater than D and D+1, we can eliminate the negative solution of the above equation. So, the final solution is:
x = [1.4D + sqrt((1.96D^2) + 2.4D)]/2D
Now, substituting D = 1 in the above equation, we get:
x = 7/3
Therefore, Amit and Deepak together can finish the work in 7/3 days.
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