Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take
8 days working 5 hours per day to complete the same task. They decide to work together to complete
this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to
work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days
Seema will work is:
Your Answer: days
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 \( \boxed{6 \, \text{days}} \).
