Sequences & Series
Work-Rate Problem — AP of Daily Work
nta_pyq_2024_apr
Grade 11
Question:
A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of $m$ is equal to:
Step-by-Step Solution
Key Concept: Original work $=17m$ units. With crashes: day 1 has $m$ systems, day 2 has $m-4$, ..., day 25 has $m-96$. Total work $=\sum_{k=0}^{24}(m-4k)=25m-4\cdot\frac{24\cdot25}{2}=25m-1200$. Set equal to $17m$.
$25m-1200=17m\Rightarrow m=150$.
Correct Answer: 1