Time and Work Question 1 - CAT 2021
One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is:
Step-by-Step Explanation
Let Rahul's hourly work output be r units/hour and Gautam's be g units/hour.
- Scenario 1:
Rahul works from 9 AM to 5 PM (8 hours) and Gautam works from 11 AM to 5 PM (6 hours).
Total Work = 8r + 6g
- Scenario 2:
Both start at 9 AM and finish 30 minutes earlier, which means they complete the work at 4:30 PM (7.5 hours total for each).
Total Work = 7.5(r + g)
= 7.5r + 7.5g
- Equate the two expressions for the total work:
8r + 6g = 7.5r + 7.5g
0.5r = 1.5g
⟹ r = 3g
Substitute r = 3g into the first equation to find the total workload in terms of g:
Total Work = 8(3g) + 6g
= 30g
Time taken by Rahul alone = Total Work/r
= 30g/3g
= 10 hours
Correct Option: B
💡 FundaMakers Tip:
Use the Work Substitution Technique instead of dragging fractions into clock times. The shift from Scenario 1 to Scenario 2 means Gautam gains 1.5 hours of working time (7.5 − 6) while Rahul gives up 0.5 hours of working time (8 − 7.5). Since the total work remains constant, Rahul's 0.5 hours of work must equal Gautam's 1.5 hours of work (0.5r = 1.5g). This logic yields the efficiency ratio instantly.