Inferring individual copy speed from a joint throughput Mr. Modi can copy 40 pages in 10 minutes. Together, Mr. Xerox and Mr. Modi copy 250 pages in 25 minutes. How many minutes will Mr. Xerox alone take to copy 36 pages?

Introduction / Context:
This problem asks you to back out an unknown worker’s rate from the combined rate and a known co-worker’s rate. Once Mr. Xerox’s pages-per-minute rate is known, time equals pages divided by rate.

Given Data / Assumptions:

• Mr. Modi: 40 pages in 10 minutes ⇒ 4 pages/min.
• Mr. Modi + Mr. Xerox: 250 pages in 25 minutes ⇒ 10 pages/min combined.
• Rates are constant during the interval.

Concept / Approach:
Combined rate = sum of individual rates. Subtract Mr. Modi’s rate to find Mr. Xerox’s rate, then compute time for 36 pages.

Step-by-Step Solution:

Verification / Alternative check:
If both worked 25 minutes at their rates (4 and 6), output is (4 + 6) * 25 = 250 pages, which matches.

Why Other Options Are Wrong:
5 minutes implies 7.2 pages/min (too high); 3 is far too high; 12 is half the needed speed.

Common Pitfalls:
Dividing 250 by 10 first (correct) but then forgetting to subtract Modi’s rate to isolate Xerox’s rate.

Final Answer:
6 minutes