ASVAB (Armed Services Vocational Aptitude Battery)Arithmetic Reasoning (AR)Medium
A squad of 9 soldiers can dig a trench in 12 hours. If 3 more soldiers join the squad, how long will it take the expanded squad to dig the same trench, assuming all soldiers work at the same rate?
- A8 hours
- B7 hours
- C10 hours
- D9 hours
Show answer & explanationAnswer & explanation
Correct answer: D. 9 hours
This is an inverse proportion problem. The total 'work units' (soldiers * hours) remain constant. 9 soldiers * 12 hours = 108 work units. With 3 more soldiers, there are 9 + 3 = 12 soldiers. So, 108 work units / 12 soldiers = 9 hours.
Why the other options are wrong
- A. This is the correct time, calculated using inverse proportion.
- B. Incorrectly assumes a linear reduction not proportional to increased workers.
- C. Incorrectly assumes a different work unit total or miscalculation.
Inverse Proportion
A relationship between two quantities where an increase in one quantity results in a decrease in the other, and vice versa, such that their product remains constant.
- Often used in 'work' problems (e.g., workers and time).
- If X and Y are inversely proportional, X × Y = k (constant).
- Increasing workers decreases time for the same amount of work.
Memory trick: More Hands, Less Time: The work product stays the same.