CAT 2025Slot 2QAQuestion & Solution
Question
Ankita is twice as efficient as Bipin, while Bipin is twice as efficient as Chandan. All three of them start together on a job, and Bipin leaves the job after 20 days. If the job got completed in 60 days, the number of days needed by Chandan to complete the job alone, is
Solution
1. Concept Used
- Topic: Time and Work — Efficiency-based work distribution
- Formula: $$\text{Total Work} = \sum (\text{Daily Work Rate} \times \text{Number of Days})$$
2. Calculation
Let Chandan's one-day work be (x). Since Bipin is twice as efficient as Chandan, Bipin's one-day work $(= 2x)$. Since Ankita is twice as efficient as Bipin, Ankita's one-day work $(= 4x)$.
All three work together for the first 20 days. Their combined daily rate $(= x + 2x + 4x = 7x)$.
Work done in the first 20 days $(= 20 \times 7x = 140x)$.
Bipin leaves after day 20. Ankita and Chandan continue for the remaining $(60 - 20 = 40)$ days. Their combined daily rate $(= 4x + x = 5x)$.
Work done in the remaining 40 days $(= 40 \times 5x = 200x)$.
Total work done $(= 140x + 200x = 340x)$.
Since Chandan completes (x) units of work per day, the number of days Chandan needs to complete the entire job alone: $$\text{Days} = \frac{340x}{x} = 340$$
3. Solution
Answer = 340 ✅
The final calculated value is 340 days.