Answer: D — The question cannot be answered due to insufficient data

Earnings $E = 5d + 2k$ where $d$ = deliveries and $k$ = km. We need $E > 500$ to "definitely" hold for the given $d$.

Why $d$ alone is not enough.

The number of kilometres $k$ depends on the routes the boy actually takes; the only constraint stated is $k \le 100$. To guarantee $E > 500$ from the value of $d$ alone, the inequality must hold even in the worst case $k = 0$, i.e. $5d > 500 \Rightarrow d > 100$.

Check each option.

For $d = 80, 85, 90$, taking $k = 0$:

• $d = 80$: $E = 400$
• $d = 85$: $E = 425$
• $d = 90$: $E = 450$

None of these exceed $500$ in the worst case, so none of A, B, or C "definitely" meets the target. The number of kilometres travelled is essential information that the question does not pin down.