1. **State the problem:** A manager plans to produce 100 bicycles using 25 persons working some hours daily. We need to find how many bicycles can be produced by 40 persons working 3 hours daily. 2. **Identify given data:** - Initial production: 100 bicycles - Initial workers: 25 persons - New workers: 40 persons - New work hours daily: 3 hours 3. **Assumption:** Production is directly proportional to the total person-hours worked. 4. **Calculate the initial person-hours:** Let the initial daily work hours be $h$. Then, $$ \text{Initial person-hours} = 25 \times h $$ 5. **Calculate the new person-hours:** $$ \text{New person-hours} = 40 \times 3 = 120 $$ 6. **Set up the proportion:** Since production is proportional to person-hours, $$ \frac{100}{25h} = \frac{x}{120} $$ where $x$ is the number of bicycles produced by 40 persons working 3 hours daily. 7. **Solve for $x$: ** $$ x = \frac{100}{25h} \times 120 = \frac{100 \times 120}{25h} = \frac{480}{h} $$ 8. **Find $h$ using the initial data:** We do not know $h$ explicitly, but since the production of 100 bicycles was achieved with 25 persons working $h$ hours daily, we can express bicycle production per person-hour as constant. Since the final answer requires knowing $h$ or the relation between $h$ and bikes/hour, let's assume the initial daily hours $h=1$ hour for calculation (since no explicit hours given initially). Then, $$ x = \frac{480}{1} = 480 $$ **Therefore, if initially 25 persons work 1 hour daily to produce 100 bicycles, then 40 persons working 3 hours daily can produce $480$ bicycles.** If initial hours differ, this proportion still holds; the answer is $\frac{480}{h}$ bicycles. **Final answer:** $480$ bicycles if $h=1$ hour daily.