Time and Work Question 2 - CAT 2022
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is:
Step-by-Step Explanation
- Convert the Time Ratio to Hourly Efficiencies:
The standalone time durations taken by Anu, Tanu, and Manu follow the ratio 5 : 8 : 10.
Let us assume a total work baseline equal to the LCM of 5, 8, and 10, which is 40 units.
Anu's efficiency = 40/5 = 8 units/hour
Tanu's efficiency = 40/8 = 5 units/hour
Manu's efficiency = 40/10 = 4 units/hour
Combined Hourly Efficiency = 8 + 5 + 4 = 17 units/hour
- Calculate Total Tank/Job Capacity:
Working together, they complete the job in 4 days at 8 hours per day, which equals:
4 × 8 = 32 total hours
Total Work Capacity = 32 hours × 17 units/hour
= 544 units
- Analyze the First Phase (Anu and Tanu):
They work together for 6 days at 6 hours 40 minutes per day.
Convert 6 hours 40 minutes into an improper fraction:
6 + 40/60 = 6 + 2/3 = 20/3 hours/day
Total active hours = 6 days × 20/3 hours/day
= 40 hours
Combined hourly efficiency of Anu and Tanu = 8 + 5 = 13 units/hour
Work completed = 40 hours × 13 units/hour
= 520 units
- Isolate Manu's Remaining Standalone Work:
Remaining Work = 544 − 520 = 24 units
Manu's required hours = 24 units/4 units/hour
= 6 hours
Correct Answer: 6
💡 FundaMakers Tip:
Whenever time parameters involve mixed fractional hours (like 6 hours 40 minutes), convert them into improper fractions (20/3) at the very start. This lines them up for clean adjustments with standard time integer variables.