Question

Rajesh can check the quality of 1000 items in 5 hours and Rakesh can complete 75\(\%\) of the same job in 3 hours. How much time is required for both of them to check 1300 items, if Rakesh stops checking after 2 hours ? 

• A. 3 hours
• B. 4 hours
• C. 2 hours
• D. 1 hours

Answer 1

The Correct Option is B

To solve this problem, we need to calculate how much work Rajesh and Rakesh individually perform, and then determine how much time both take to finish checking 1300 items, given that Rakesh stops checking after 2 hours.

1. We are told that Rajesh can check 1000 items in 5 hours. Thus, his work rate is: \(\frac{1000}{5} = 200\) items per hour.
2. Rakesh can complete 75% of the job (which is 1000 items) in 3 hours. This means he checks: \(\frac{75}{100} \times 1000 = 750\) items in 3 hours.
   • Thus, Rakesh's work rate is: \(\frac{750}{3} = 250\) items per hour.
3. Both Rajesh and Rakesh work together, but Rakesh stops after 2 hours.
4. In those 2 hours, the combined output of Rajesh and Rakesh is:
   • Rajesh: \(200 \times 2 = 400\) items
   • Rakesh: \(250 \times 2 = 500\) items
   • Total: \(400 + 500 = 900\) items
5. After Rakesh stops, 400 items are still left to be checked (since they completed 900 out of 1300 items).
6. Now, only Rajesh continues to work. To find out how much time Rajesh takes to check the remaining 400 items: \(\frac{400}{200} = 2\) hours.

Thus, the total time required for both to check 1300 items is: 2 hours (initial work together) + 2 hours (Rajesh alone) = 4 hours.

Therefore, the correct answer is: 4 hours.