How to Solve Compound Proportion Problems
Solve compound proportion aptitude problems combining workers, days, hours and work, with a worked example and practice questions with answers.
Expected Interview Answer
Compound proportion problems involve multiple varying quantities (like workers, days, hours, and units of work) linked together, solved by setting up a single equation where the product of all quantities on one side stays proportional to the product on the other, using the rule of “more workers means less time, more hours means less days” to decide direct or inverse relationships for each pair.
Identify every quantity involved (people, days, hours per day, quantity of work, machines, etc.) and, for each pair, ask: if this quantity increases, does the target quantity increase (direct) or decrease (inverse)? More workers or more hours per day directly reduce the days needed (inverse relation to days), while more work to be done directly increases the days needed (direct relation to days). Combine every relation into one compound equation of the form: Product of quantities in Scenario 1 (with inverse ones flipped) equals the same product in Scenario 2. Cross-multiply and solve for the unknown, always sanity-checking that the direction of change makes physical sense.
- A single compound equation handles any number of varying factors at once
- The direct/inverse test for each pair prevents relationship-direction errors
- Generalizes work-time-people problems, machine problems, and rate problems uniformly
AI Mentor Explanation
If a groundstaff of a certain size preps a certain number of pitches in a set number of days working a set number of hours daily, then doubling the staff and doubling the daily hours while doubling the number of pitches to prepare changes the days needed in a compound way — more staff and more hours reduce days (inverse), but more pitches increase days (direct). Compound proportion problems combine all these direct and inverse relationships into a single equation to solve for the unknown days.
Worked example (workers, days, hours, work)
Scenario 1
- 12 men, 8 hrs, 10 days
- work = 1 unit
Scenario 2
- 15 men, 6 hrs, D days
- work = 2 units
Solve
- (12×8×10)/1=(15×6×D)/2
- D ≈ 21.33 days
Step-by-Step Explanation
Step 1
List every varying quantity
Workers, days, hours per day, amount of work, machines, etc.
Step 2
Classify each as direct or inverse
Ask: does increasing this quantity increase or decrease the target?
Step 3
Build the compound equation
(Product of quantities, inverse ones as reciprocals) stays equal across both scenarios.
Step 4
Solve and sanity-check
Isolate the unknown, then confirm the direction of change matches intuition.
What Interviewer Expects
- Correct identification of every varying quantity in the problem
- Correct direct/inverse classification for each quantity relative to the unknown
- Accurate setup of the compound proportion equation across two scenarios
- Sanity-checking the final answer against the expected direction of change
Common Mistakes
- Misclassifying a direct relationship as inverse or vice versa
- Forgetting to include one of the varying quantities in the equation
- Mixing up which scenario's values go in the numerator versus denominator
- Not adjusting the equation when “amount of work” itself changes between scenarios
Best Answer (HR Friendly)
“The trick with compound proportion is to list out every quantity that is changing — people, hours, days, amount of work — and for each one ask whether increasing it would increase or decrease the answer you are solving for. More workers or more hours per day should reduce the number of days needed, so those are inverse, while more total work to do should increase the days needed, so that is direct. Once you have tagged each factor correctly, you multiply everything together in one equation across the two scenarios and solve for the unknown.”
Follow-up Questions
- How would you handle a compound proportion problem involving machines with different efficiencies?
- How do you set up the equation if the amount of work is expressed as a ratio rather than a multiple?
- How would you extend this to a scenario with three different work situations instead of two?
- How do you verify your direct/inverse classification before finalizing an equation?
MCQ Practice
1. 8 men working 6 hours a day build a wall in 10 days. How many days will 12 men working 8 hours a day take to build the same wall?
8×6×10 = 12×8×D → 480 = 96D → D = 5 days.
2. If 6 machines produce 60 units in 5 days, how many days will 10 machines take to produce 150 units?
(6×5)/60 = (10×D)/150 → 0.5 = 10D/150 → D = 7.5 days.
3. In a compound proportion problem, if the amount of work doubles while all other factors stay the same, the days required will?
Amount of work is directly proportional to days needed, so doubling the work doubles the days required.
Flash Cards
What is the first step in a compound proportion problem? — List every varying quantity involved in the scenario.
How do more workers affect days needed? — Inversely — more workers reduce the days required.
How does more total work affect days needed? — Directly — more work increases the days required.
General compound proportion equation form? — Product of Scenario 1 quantities (inverse ones as reciprocals) = same product for Scenario 2.