Inferring a second worker’s rate and then combining: Sonu can complete a job in 20 days. He works alone for some days until 25% of the job is finished. Abhijeet then works alone and finishes the remaining work in 10 days. If Sonu and Abhijeet work together from the start, how many days will they take to finish the whole job?

Introduction / Context:
This problem involves first deducing Abhijeet’s solo rate from the information about the remaining work and then computing the combined time if both worked together throughout. It tests rate inference and combined-rate application.

Given Data / Assumptions:

• Sonu’s time alone = 20 days ⇒ rate_S = 1/20 job/day.
• When Sonu stops, 25% is done ⇒ 75% remains.
• Abhijeet finishes the remaining 75% in 10 days ⇒ rate_A = 0.75 / 10 = 0.075 job/day.

Concept / Approach:
Once both rates are known, the combined rate is the sum. The total time for one job at the combined rate is T = 1 / (rate_S + rate_A).

Step-by-Step Solution:
rate_S = 1/20 = 0.05rate_A = 0.75 / 10 = 0.075Combined rate = 0.05 + 0.075 = 0.125 job/dayTogether time T = 1 / 0.125 = 8 days

Verification / Alternative check:
Check: In 8 days at 0.125 job/day, they complete exactly 1 job. Also, Abhijeet’s inferred full-time to complete alone would be 1 / 0.075 ≈ 13.33 days, which is consistent with finishing 75% in 10 days.

Why Other Options Are Wrong:

• 6 and 10 days correspond to incorrect combined rates.
• 12 days is too slow compared to the derived 8 days.

Common Pitfalls:

• Mistaking 25% as the remaining work instead of the completed part.
• Forgetting that rates add when people work together.

Final Answer:
8