12 men can finish a job in 18 days working 8 hours a day. How many days will 16 men take working 9 hours a day?
12 days. Total work in man-hours = 12 x 18 x 8 = 1,728. With 16 men at 9 hours a day, daily output = 144 man-hours, so days = 1,728 / 144 = 12.
Explain it simply
Measure work in man-hours, the way a contractor quotes labour for building a hostel block: one man working one hour is one unit. The job needs a fixed number of these units no matter how you split them. More men or longer days means fewer days. So M1 x D1 x H1 = M2 x D2 x H2 for the same job.
Example
Question: 12 men x 18 days x 8 hours = same job as 16 men x D days x 9 hours.
- Total work = 12 x 18 x 8 = 1,728 man-hours.
- Per day now: 16 x 9 = 144 man-hours.
- D = 1,728 / 144 = 12 days.
If the second job is a different size, divide each side by the work: M1 D1 H1 / W1 = M2 D2 H2 / W2. For example, if the second job is 1.5 times as large, D = 12 x 1.5 = 18 days.
const work = 12 * 18 * 8;
console.log(work / (16 * 9)); // Output: 12
console.log((work * 1.5) / (16 * 9)); // Output: 18What to say in the interview
"I measure the job in man-hours: 12 times 18 times 8 is 1,728. Sixteen men at nine hours give 144 a day, so it takes 12 days. If the amount of work changes, I scale by it too."
Common mistakes
- Using direct proportion between men and days (more men, more days).
- Ignoring the hours-per-day factor.