Answer :
Ghel takes 15 minutes to arrange 100 books, while Ghel and Mike together take 8 minutes to arrange 80 books. Therefore, it would take Mike 2.5 minutes to arrange 50 books by himself.
Let's assume that Ghel's rate of arranging books is Rg books per minute, and Mike's rate is Rm books per minute. From the given information, we know that Ghel takes 15 minutes to arrange 100 books, so we can write the equation 15Rg = 100. Simplifying this equation, we find that Rg = 100/15 = 20/3 books per minute.
Next, we know that Ghel and Mike together take 8 minutes to arrange 80 books. This can be expressed as (8Rg) + (8Rm) = 80. Substituting the value of Rg from the previous equation, we have (8 * 20/3) + (8Rm) = 80. Simplifying further, we get (160/3) + (8Rm) = 80.
To find out how long it will take Mike to arrange 50 books on his own, we can set up the equation Rm * Tm = 50, where Tm represents the time in minutes. Rearranging the equation, we have Tm = 50 / Rm.
Now, substituting the value of Rm from the previous equation, we get Tm = 50 / [(80 - 160/3)/8]. Simplifying this expression, we find Tm = 50 / (80/3 - 20/3) = 50 / (60/3) = 50 / 20 = 2.5.
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