Time and Work Question 3 - CAT 2023
Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is:
Step-by-Step Explanation
- Analyze the Work Deficit Balance:
Gautam and Suhani's combined normal daily work output matches a 20-day completion rate.
One day, Gautam reduces his work output to 60%, creating a 40% drop in his daily contribution. Suhani increases her output to 150%, creating a 50% increase in her contribution. Since this adjustment exactly maintains their schedule, Suhani's increase perfectly matches Gautam's decrease:
40% of Gautam = 50% of Suhani
0.40G = 0.50S
âźą S/G = 4/5
- Calculate the standalone completion time:
This ratio shows that Gautam is the faster worker. Let us define their daily efficiencies as:
G = 5x units/day
S = 4x units/day
Combined Daily Efficiency = 5x + 4x = 9x units/day
Total Work (W) = 20 days Ă— 9x units/day
= 180x units
Time taken by Gautam alone = 180x/5x
= 36 days
Correct Answer: 36
đź’ˇ FundaMakers Tip:
Use the Work Balance Shortcut! If one worker's drop is balanced out by another worker's increase, their efficiency ratio is simply the inverse of their percentage changes (40% : 50% âźą 5 : 4). This approach bypasses simultaneous fractional setups entirely.