Worker A completes 75% of a certain job in 25 days. He then calls in worker B, and together they finish the remaining 25% of the work in 5 days. How many days would B alone require to complete the entire job working at his own constant rate?

Introduction / Context:
This time and work question involves one worker starting a job, then another worker joining later to help finish it. We are given how much of the job A completes alone and how long A and B together take to finish the remainder. Using this, we must deduce B's individual efficiency and then find how long B would take to do the entire job alone.

Given Data / Assumptions:

• A completes 75% of the job in 25 days.
• The remaining 25% is finished by A and B working together in 5 days.
• Work rates remain constant throughout.
• The total work is one complete job.
• We are to find B's solo time for the entire job.

Concept / Approach:
We interpret the 75% completion in 25 days as A's rate. Then, since the remaining 25% is done by A and B together in 5 days, we interpret that as their combined rate. The difference between the combined rate and A's rate gives B's rate. Finally, we invert B's rate to find the time B would require to complete the entire job alone.

Step-by-Step Solution:
Let total work = 1 unit.A completes 75% = 3 / 4 of the job in 25 days.So A's rate = (3 / 4) / 25 = 3 / 100 work per day.Remaining work = 1 - 3 / 4 = 1 / 4.A and B together complete 1 / 4 of the job in 5 days.Combined rate of A and B = (1 / 4) / 5 = 1 / 20 work per day.So B's rate = (A + B rate) - A's rate = 1 / 20 - 3 / 100.Compute 1 / 20 = 5 / 100, so B's rate = 5 / 100 - 3 / 100 = 2 / 100 = 1 / 50 work per day.Therefore, time taken by B alone to do the entire job = 1 / (1 / 50) = 50 days.

Verification / Alternative check:
Check consistency: In 25 days, A does 25 * 3 / 100 = 75 / 100 = 3 / 4 of the work. There is 1 / 4 left. Together, A and B work for 5 days. A contributes 5 * 3 / 100 = 15 / 100, and B contributes 5 * 1 / 50 = 5 / 50 = 10 / 100. Total from this phase is 25 / 100 = 1 / 4. Summing 3 / 4 + 1 / 4 = 1, so the work is exactly completed and the rates are consistent.

Why Other Options Are Wrong:
Twenty four or 37.5 days would imply that B is significantly faster than the rate implied by the combined phase and would not maintain the correct division of work. Eighty days suggests B is much slower than A, which does not fit with the observed completion when they work together. Only 50 days matches the rate difference and the timing of the remaining work.

Common Pitfalls:
It is easy to confuse the fraction of work completed by A alone with the fraction completed jointly. Some learners incorrectly assume that A and B share the remaining work equally in the second phase. Others forget to convert percentages into fractions. Always express all portions of work as fractions of the whole and proceed step by step when combining rates.

Final Answer:
Worker B alone would complete the entire job in 50 days.