This problem is based on Work Rate Concept.
We will be using two concepts\formulas in this problem:
1. Rate * Time = Work Done
2. When two people work together then their rates get added up.
Let Rate of W is "W" and Rate of V is "V"
Worker W produces n units in 5 hour
Using, Rate * Time = Work Done we have
W * 5 = n => W = \(\frac{n}{5}\) ...(1)
Workers V and W, working independently but at the same time, produce n units in 2 hours
=> (V + W) * 2 = n [ as V and W are working together so their rates will get added up ]
=> V + W = \(\frac{n}{2}\) ....(2)
(2) - (1) we have
V + W - W = \(\frac{n}{2}\) - \(\frac{n}{5}\) = \(\frac{5n}{10}\) - \(\frac{2n}{10}\)
=> V = \(\frac{3n}{10}\)
How long would it take V alone to produce n units
V * t = n
=> \(\frac{3n}{10}\) * t = n
=> t = \(\frac{10}{3}\)hrs = \(\frac{10 * 60}{3}\) mins = 200 mins = 3hrs 20mins
So, answer will be D
Hope it helps!
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