Increasing workforce in steps: 15 men could finish a piece of work in 210 days at the original staffing. However, at the end of every 10 days, 15 additional men are employed (i.e., workforce grows by +15 after each 10-day block). How many days will it now take to finish the work?

Introduction / Context:
This is a variable-workforce problem where staffing increases in equal steps. We accumulate man-days over each 10-day block until total man-days equal the original job size.

Given Data / Assumptions:

• Original completion: 15 men * 210 days ⇒ total job = 3150 man-days.
• Every 10 days, add 15 more men: 15, 30, 45, … per block.

Concept / Approach:
Compute man-days per block and sum the arithmetic series until we reach 3150 man-days.

Step-by-Step Solution:
Block 1 (days 1–10): 15 * 10 = 150 man-days.Block 2: 30 * 10 = 300; Block 3: 45 * 10 = 450; etc.After n blocks: total = 150 * (1 + 2 + ... + n) = 150 * n(n + 1)/2 = 75 n(n + 1).Set 75 n(n + 1) = 3150 ⇒ n(n + 1) = 42 ⇒ n = 6.Time = 6 blocks * 10 days = 60 days.

Verification / Alternative check:
Sum explicitly: 150 + 300 + 450 + 600 + 750 + 900 = 3150 man-days → exact match.

Why Other Options Are Wrong:
30, 35, 50, and 70 days mis-sum the arithmetic series or total job size.

Common Pitfalls:
Assuming linear time shrinkage without checking cumulative man-days; forgetting each block lasts exactly 10 days.

Final Answer:
60 days