Time & Work CAT 2024 Actual Questions

Detailed Solution:
Step 1: Work rates of Renu and Seema
- Renu's total hours for the task: \( 15 \times 4 = 60 \, \text{hours} \).
- Renu's work rate: \( \frac{1}{60} \, \text{tasks/hour} \).
- Seema's total hours for the task: \( 8 \times 5 = 40 \, \text{hours} \).
- Seema's work rate: \( \frac{1}{40} \, \text{tasks/hour} \).

Step 2: Collaborative work conditions
- Renu works for \( 2x \, \text{days} \) at \( 2 \, \text{hours/day} \):
\[ \text{Work by Renu} = \frac{2x}{60} = \frac{x}{30}. \] - Seema works for \( x \, \text{days} \) at \( 4 \, \text{hours/day} \):
\[ \text{Work by Seema} = \frac{4x}{40} = \frac{x}{10}. \]
Step 3: Total work equals one task
\[ \frac{x}{30} + \frac{x}{10} = 1. \] Simplify the equation:
\[ \frac{x}{30} + \frac{3x}{30} = 1 \quad \implies \quad \frac{4x}{30} = 1 \quad \implies \quad x = \frac{30}{4} = 6 \, \text{days}. \]
Final Answer: Seema will work for \( \boxed{6 \, \text{days}} \).