Determine Worker Counts from Production Ratios
Company: Barclays
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
## Interview Prompt
A factory produces 2,160 fasteners in one day. The ratio of nails to screws is
2:1. A worker assigned to nails produces 18 nails per day, while a worker assigned
to screws produces 24 screws per day. Assuming each worker makes only one product
and all workers have the stated output, how many workers make nails, how many make
screws, and how many workers are there in total?
### Constraints & Assumptions
- The 2:1 ratio applies to item counts, not worker counts.
- All 2,160 items are either nails or screws.
- Worker counts must be nonnegative integers.
### Clarifying Questions to Ask
- Does the production total refer to one day?
- May a worker split time between nails and screws?
- Are the stated per-worker outputs exact?
### What a Strong Answer Covers
- Correct conversion of the item ratio into nail and screw quantities.
- Separate division by the two per-worker productivity rates.
- An arithmetic check that reconstructed production totals 2,160 items.
### Follow-up Questions
- How would the answer change if workers could split a day between products?
- What consistency condition would reveal that a stated total is impossible?
- If one nail worker is absent, how many additional nail-worker days are needed?
Overview: Solve a production-ratio word problem by converting the 2-to-1 item ratio into nail and screw quantities before applying each worker's daily output. The answer must yield separate integer worker counts and their total without confusing product ratios with staffing ratios.
Community answers
Answer by LanceOak7126
My approach would be to use the letters n and s to represent the number of nails and screws, respectively. Using the ratio, there are three parts: The number of nail workers equals the number of nails divided by 18, and the number of screw workers equals the number of screws divided by 24. The total number of workers is equal to the number of nail workers plus the number of screw workers. 2,160 = (nail workers)18 + (screw workers)24. Using these equations and simplifying them, I found the following solution.
2,160 = (nail workers × 18) + (screw workers × 24)
2,160 = 6 ((nail workers × 3) + (screw workers × 4))
360 = (nail workers × 3) + (screw workers × 4)
360 = ((number of nails) / 18) × 3 + ((number of screws) / 24) × 4
360 = (number of nails + number of screws) / 6
2,160 = number of nails + number of screws
2,160 = 2 × (number of screws) + number of screws
2,160 = 3 × (number of screws)
720 = number of screws
1,440 = number of nails
Nail workers = 1,440 / 18
Nail workers = 80
Screw workers = 720/24 = 30
Total workers = 80 + 30 = 110