Question 4Time & Work
Pooja alone would need 12 days at 5 hours a day to finish a piece of work, while Nisha alone would need 10 days at 6 hours a day to finish the same work. They both contribute to completing the same piece of work, at constant hourly rates. Nisha puts in twice as many hours per day as Pooja, while Pooja works twice as many days as Nisha. If Pooja works 3 hours a day, how many days does Nisha work?
Answer and solution
Correct answer: 5
Solution
Answer: 5
1. Pooja needs 12×5=60 hours alone. Nisha needs 10×6=60 hours alone. Each hourly rate is 1/60 of the job.
2. Pooja works 3 hours daily; Nisha works twice this, 6 hours daily. Let Nisha work d days and Pooja 2d days.
3. Their combined work is (3×2d)/60+(6d)/60=1.
4. Thus 12d=60 and d=5. Check: each completes 30 hours, together one full job.
Why this method works:
Convert each person’s solo schedule into hours before comparing their efficiencies:12×5 and 10×6 both equal 60. Their daily outputs differ only because they work different numbers of hours, not because one has a faster hourly rate.
Independent check and common trap:
If Nisha works 5 days at 6 hours she contributes 30 hours. Pooja works 10 days at 3 hours, also 30 hours. Together their 60 effective hours complete the job. The answer asks for Nisha’s days, not Pooja’s 10 days.
Apply: Both need 60 working hours, so hourly rates are equal. Their total hours are also equal (3×2d=6d). Each supplies half the work: Nisha needs 30/6=5 days.
Check: If Nisha works 5 days at 6 hours she contributes 30 hours. Pooja works 10 days at 3 hours, also 30 hours. Together their 60 effective hours complete the job. The answer asks for Nisha’s days, not Pooja’s 10 days.
1. Pooja needs 12×5=60 hours alone. Nisha needs 10×6=60 hours alone. Each hourly rate is 1/60 of the job.
2. Pooja works 3 hours daily; Nisha works twice this, 6 hours daily. Let Nisha work d days and Pooja 2d days.
3. Their combined work is (3×2d)/60+(6d)/60=1.
4. Thus 12d=60 and d=5. Check: each completes 30 hours, together one full job.
Why this method works:
Convert each person’s solo schedule into hours before comparing their efficiencies:12×5 and 10×6 both equal 60. Their daily outputs differ only because they work different numbers of hours, not because one has a faster hourly rate.
Independent check and common trap:
If Nisha works 5 days at 6 hours she contributes 30 hours. Pooja works 10 days at 3 hours, also 30 hours. Together their 60 effective hours complete the job. The answer asks for Nisha’s days, not Pooja’s 10 days.
G Strategy shortcut
Spot: Time and Work.Apply: Both need 60 working hours, so hourly rates are equal. Their total hours are also equal (3×2d=6d). Each supplies half the work: Nisha needs 30/6=5 days.
Check: If Nisha works 5 days at 6 hours she contributes 30 hours. Pooja works 10 days at 3 hours, also 30 hours. Together their 60 effective hours complete the job. The answer asks for Nisha’s days, not Pooja’s 10 days.
G Strategy: Spot: Time and Work. Apply: Both need 60 working hours, so hourly rates are equal. Their total hours are also equal (3×2d=6d). Each supplies half the work: Nisha needs 30/6=5 days. Check: If Nisha works 5 days at 6 hours she contributes 30 hours. Pooja works 10 days at 3 hours, also 30 hours. Together their 60 effective hours complete the job. The answer asks for Nisha’s days, not Pooja’s 10 days.