A group of 12 workers can build a wall in 15 days working 8 hours per day. How many days will 18 workers take to build the same wall if they work 6 hours per day?

hard 5 marks Class 8 · Mathematics · Direct and Inverse Proportions

Answer

13 1/3 days

The correct answer is 13 1/3 days — Solve: $Days = 1440/108 = 13. \overline{3} = 13, \frac{1}{3}$ days.

Step-by-step solution

Let the total work $W$ be measured in worker‑hours.
Compute $W$ for the first scenario: $W = 12 workers \times 8 hrs/day \times 15 days = 1440$ worker‑hours.
For the second scenario the available work per day is $18 \times 6 = 108$ worker‑hours/day.
Set up the equation $108 \times Days = 1440$ to find the required days.
Solve: $Days = 1440/108 = 13. \overline{3} = 13, \frac{1}{3}$ days.

Common mistake: Using the product of workers and days while ignoring hours per day, or misapplying the direct proportion formula.

Concept tested: Inverse Proportion (workers, hours, days)