Time and Work Question 1 - CAT 2024
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:
Step-by-Step Explanation
- Analyze the Work Hours:
Let R be the work done by Renu per hour and S be the work done by Seema per hour.
Total Work = 15 days Ă— 4 hours/day Ă— R
= 60R
Total Work = 8 days Ă— 5 hours/day Ă— S
= 40S
60R = 40S
âźą S = 1.5R
- Apply the New Working Conditions:
Let Seema work for X days.
Renu agrees to work for double the number of days as Seema, so Renu works for 2X days.
Renu works 2 hours per day.
Seema works for double the number of hours per day as Renu, so Seema works for 4 hours per day.
- Formulate the Total Work Equation:
Work by Renu = 2X days Ă— 2 hours/day Ă— R
= 4XR
Work by Seema = X days Ă— 4 hours/day Ă— S
= 4XS
Substitute S = 1.5R into Seema's work expression:
Work by Seema = 4X Ă— 1.5R
= 6XR
Total Combined Work = 4XR + 6XR
= 10XR
Equate this to the total work baseline (60R):
10XR = 60R
âźą X = 6 days
The number of days Seema will work is 6.
Correct Answer: 6
đź’ˇ FundaMakers Tip:
When managing multi-variable constraints like interchanged or doubled parameters, always break them down into absolute independent units (in this case, total hours). Establishing the direct relationship between the individual hourly efficiencies (S = 1.5R) simplifies the dynamic arrangement down to a single-variable linear equation.
Time and Work Shortcuts & Tricks
Importance of PYQs for Time and Work Preparation
- Understand CAT Pattern: Know how CAT frames questions.
- Identify Question Types: Efficiency, combined work, wages, etc.
- Analyse Difficulty: Understand the actual CAT difficulty level.
- Track Trends: Identify year- and slot-wise patterns.
- Improve Speed: Learn faster solving approaches.
- Find Weak Areas: Identify concepts requiring more practice.
- Avoid Mistakes: Learn from common errors.
- Build Confidence: Get comfortable with actual CAT-level questions.