Kamran started a certain work at 10 am and Umar joined him three hours later. They then together completed the work at 6 pm on the same day. Instead, if both had started at 10 am and worked together, the work would have been completed at 5 pm. How long (In hours) would Umar alone take to complete the entire work?

Let the efficiencies of Kamran and Umar be K and U, and let the total work be W. The first condition states that Kamran works for 8 hours and Umar works for 5 hours, giving the equation 8K plus 5U equals W. The second condition states that if they work together for 7 hours, the work is completed, giving the equation 7K plus 7U equals W. Setting the two equations equal gives 8K plus 5U equals 7K plus 7U. This simplifies to K equals 2U. Substituting this into the second equation gives 7 times 2U plus 7U equals W, which means 21U equals W. Therefore, Umar alone would take 21 hours to complete the entire work. The correct answer is 21.

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