Question

Sunil Makihija can check the quality of 1000 items in 5 hours and Nilesh Desai can complete 75% of the same job in 3 hours. How much time is required for both of them to check 1300 items if Nilesh stops checking after 2 hours? 
 

• A. 2 hours
• B. 4 hours
• C. 3 hours
• D. 6 hours 30 minutes
• E. 4 hours 15 minutes

Hint:

Break such problems into phases: work done together, then work done individually.

Answer 1

The Correct Option is B

Step 1: Finding Individual Rates:
Sunil's rate = \(\frac{1000}{5} = 200\) items/hour.
Nilesh completes 75% of 1000 = 750 items in 3 hours.
Nilesh's rate = \(\frac{750}{3} = 250\) items/hour.

Step 2: Work Done in First 2 Hours:
Both work for 2 hours:
Work done = \(2 \times (200 + 250) = 2 \times 450 = 900\) items.

Step 3: Remaining Work:
Total to check = 1300 items.
Remaining = \(1300 - 900 = 400\) items.
After 2 hours, Nilesh stops. Only Sunil works.
Time for Sunil to complete remaining = \(\frac{400}{200} = 2\) hours.

Step 4: Total Time:
Total time = \(2 + 2 = 4\) hours.