Multiple choice

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

  1. 11.5

  2. 10

  3. 12.5

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let R and G be rates. R works 8 hours (9AM to 5PM), G works 6 hours. R*8 + G*6 = 1. If both work 7.5 hours (30 mins earlier), (R+G)*7.5 = 1. Solving the system: 8R + 6G = 7.5R + 7.5G -> 0.5R = 1.5G -> R = 3G. Substitute: (3G)*8 + 6G = 1 -> 30G = 1 -> G = 1/30. R = 3/30 = 1/10. Rahul takes 10 hours.

AI explanation

Using the work formula, let Rahul's hourly rate be 1/x and Gautam's be 1/y. Working together from 9 AM, they take x times y divided by (x plus y) hours, and finishing 30 minutes earlier means the combined time is 7.5 hours. When Rahul works alone for 2 hours and then with Gautam for 6 hours, the work equation is 2/x plus 6 divided by 7.5 equals 1. Multiplying by x gives 2 plus 0.8x equals x, meaning x is 10. The result is 10 hours.

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