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2014-11-11T04:51:46+05:30

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Tank capacity = V  

Tap 1  filling duration = T   =>  flow rate = V/T
Tap 2 filling duration = T+10  =>  flow rate = V/(T+10)

When two taps are filling together, flow rate =  V (1/T  + 1/(T+10) )
            = V * (2 T+10) / (T² +10 T) 
      So     Time to fill tank = (T²+10T) / (2T+10)  = 75/8

       =>  8T² + 80 T = 150 T + 750
          
             8 T² - 70 T - 750 = 0

             4 T² - 35 T - 375 = 0
 
              T = [ 35 +- √(35² + 6000) ] / 8

            T = 15 hours     The bigger tap
           Smaller tap  takes 25  hours  to fill.

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