Peanut Harvest

Answer: $\frac15$


Working out how much is left after each stage
After A has eaten the fraction left is $\frac{1}{2}$.

B eats $\frac{1}{3}$ of this which leaves $\frac{1}{2} - (\frac{1}{2} \times \frac{1}{3}) = \frac{1}{2} - \frac{1}{6}= \frac{1}{3}$.

C eats $\frac{1}{4}$ which leaves $\frac{1}{3} - (\frac{1}{3} \times \frac{1}{4}) = \frac{1}{3} - \frac{1}{12} = \frac{1}{4}$.

D eats $\frac{1}{5}$ which similarly leaves $\frac{1}{5}$.


Multiplying the fractions not eaten
A eats $\frac12$ and leaves $\frac12$
B eats $\frac13$ so leaves $\frac23$
And so on, so the fraction left at the end will be $\frac12\times\frac23\times\frac34\times\frac45=\frac15$ since most numerators cancel with the previous denominator.