Answer:
The initial momentum of the person and balloon is zero. Hence when the person climbs, the balloon will come down with such a velocity \[\upsilon \] that the total momentum be still zero. The velocity of the person dative to earth is (\[\upsilon -u\]). Hence \[m(\upsilon -u)-Mu=0\] or \[u=\frac{mu}{M+m}.\]
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