If 5 workers can complete a task in 12 days, how many days will 8 workers take to complete the same task?

easy 2 marks Class 8 · Mathematics · Direct and Inverse Proportions

Answer

7.5 days

The correct answer is 7.5 days — Solve for $Days_{2}$ : $Days_{2} = 12 \times \frac{5}{8} = 7.5$ days.

Step-by-step solution

Set up the proportion based on inverse relationship: $\frac{Days _{1}}{Workers _{1}} = \frac{Days _{2}}{Workers _{2}}$ .
Replace known values: $\frac{12}{5} = \frac{Days _{2}}{8}$ .
Solve for $Days_{2}$ : $Days_{2} = 12 \times \frac{5}{8} = 7.5$ days.

Common mistake: Mixing up which variable is inversely proportional; using

\frac{Workers _{1}}{Days _{1}} = \frac{Workers _{2}}{Days _{2}}

instead.

Concept tested: Direct/Inverse Proportion