A can complete a work in 15 days and B can complete a work in 25 days. If they start work together and B leaves 7 days before com…

Question

A can complete a work in 15 days and B can complete a work in 25 days. If they start work together and B leaves 7 days before completion, then the work will be completed in how many days?

1. A. 16 days
2. B. 14 days
3. C. 12 days (Correct answer)
4. D. 10 days

Correct Answer

Option C — C

Detailed Solution & Explanation

The correct answer is Option C.

Key Points

• A's rate = 1/15 per day, B's rate = 1/25 per day.
• Let the work finish in n days.
• B leaves 7 days before completion, so B works for (n − 7) days while A works all n days:
• n·(1/15) + (n − 7)·(1/25) = 1
• Multiply by 75: 5n + 3(n − 7) = 75
• 5n + 3n − 21 = 75
• 8n = 96 → n = 12.
• So the work is completed in 12 days.

Exam Tip

• when someone leaves early, let total time = n, express each person's working days in terms of n, sum their (rate × days) contributions to 1, and solve.

Additional Information

• When one worker leaves partway, let the total duration be d days: the one who stays throughout contributes d/15, and the other contributes only for the days actually worked.
• Set the sum of the contributions to 1 and solve for d.
• Always confirm which worker leaves and after how many days — misreading that detail is the commonest error in this question type.