Question
There are four pipes A, B, C and D where A and B are
used to fill the tank and C and D are used to empty the tank. Pipe A and C together can fill the tank in (a+9) hours. Pipe B alone can fill 75% of the tank in (a-1.5) hours. The efficiency of pipe C is 25% less than that of pipe B. Pipe D alone can empty half of the tank in (a-3) hours. The efficiency of pipe A is 50% more than that of pipe B. Find out the time taken by pipe A and D together to fill the empty tank completely.Solution
LetтАЩs assume the total capacity of the tank is 72 units. The efficiency of pipe A is 50% more than that of pipe B. LetтАЩs assume the efficiency of pipe B is тАШ4yтАЩ. efficiency of pipe A = 4y of (100+50)% = 4y of 150% = (4y x 150)/100 = 600y/100 = 6y units/hour The efficiency of pipe C is 25% less than that of pipe B. efficiency of pipe C = (100-25)% of (efficiency of pipe B) efficiency of pipe C = 75% of (efficiency of pipe B) efficiency of pipe C = 75% of 4y = -3y units/hour [Here the negative sign represents the pipe used to empty the tank.] Pipe A and C together can fill the tank in (a+9) hours. (a+9)x(6y-3y) = 72 (a+9)x3y = 72┬а ┬а Eq.(i) Pipe B alone can fill 75% of the tank in (a-1.5) hours. Time taken by Pipe B alone to fill 100% of the tank = ((a-1.5)/75)x100 = ((a-1.5)/3)x4 So ((a-1.5)/3)x4x4y = 72┬а ┬а Eq.(ii) We can say that Eq.(i) = Eq.(ii). (a+9)x9 = (a-1.5)x16 9a+81 = 16a-24 16a-9a = 81+24 7a = 105 a = 15 Pipe D alone can empty half of the tank in (a-3) hours. Time taken by Pipe D alone to empty the tank = 2x(a-3) So 2x(a-3)x(efficiency of Pipe D) = 72 Put the value of тАШaтАЩ in the above equation. 2x(15-3)x(efficiency of Pipe D) = 72 2x12x(efficiency of Pipe D) = 72 24x(efficiency of Pipe D) = 72 efficiency of Pipe D = -3 units/hour [Here the negative sign represents the pipe used to empty the tank.] Put the value of тАШaтАЩ in Eq.(i) to obtain the value of тАШyтАЩ. (15+9)x3y = 72 24x3y = 72 y = 1 Time taken by pipe A and D together to fill the empty tank completely = capacity of tank/(efficiency of pipe A and D together) = 72/(6y-3) Put the value of тАШyтАЩ in the above equation. = 72/(6-3) = 72/3 = 24 hours
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рд╕реЗ рдХреМрди рд╕реА рднрд╛рд╖рд╛┬ардЖрдард╡реАрдВ рдЕрдиреБрд╕реВрдЪреА ┬ардореЗрдВ рдирд╣реАрдВ рд╣реИ ?
рдХрд┐рд╕реА рдХрд░реНрдордЪрд╛рд░реА/рдЕрдзрд┐рдХрд╛рд░реА рдХреЛ рдХрд┐рд╕ рдЖрдзрд╛рд░ рдкрд░ рд╣рд┐рдВрджреА рдореЗрдВ рдкреНрд░рд╡реАрдг рдорд╛рдия┐╜...
рдореИрддреИ рдорд╛рдпреЗрдХ рд▓рд┐рдкрд┐ рдХрд┐рд╕ рд░рд╛рдЬреНрдп рдХреА рдЖрдзрд┐рдХрд╛рд░рд┐рдХ рднрд╛рд╖рд╛ рд▓рд┐рдЦрдиреЗ рдореЗрдВ рдк...
рдХреЗрдВрджреНрд░ рд╕рд░рдХрд╛рд░ рдХреЗ рд╕рднреА рдлреЙрд░реНрдо, рдирд╛рдо рдкрддреНрд░ ,рд╕реВрдЪрдирд╛ рдкрддреНрд░ ,рд╢реАрд░реНрд╖, я┐╜...
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рд╢рдмреНрджреЛрдВ рдореЗрдВ рд╕реЗ convention рдХрд╛ рд╕рд╣реА рдкрд░реНрдпрд╛рдп рдирд╣реАрдВ рд╣реИ ?
рднрд╛рд╖рд╛рдИ рдЕрд▓реНрдкрд╕рдВрдЦреНрдпрдХ рд╡рд░реНрдЧреЛрдВ рдХреЗ рд▓рд┐рдП рд╡рд┐рд╢реЗрд╖ рдЕрдзрд┐рдХрд╛рд░реА рдХрд╛ рдкреНрд░рд╛рд╡рдзрд╛рди...
рдирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдкреНрд░рд╢реНрди рдореЗрдВ рдПрдХ рд╣рд┐рдВрджреА рдХрд╛ рд╢рдмреНрдж рджрд┐рдпрд╛ рдЧрдпрд╛ рд╣реИред рдЙрд╕рдХреЗ рд▓...
рд╕рд┐рдиреНрдзреА рднрд╛рд╖рд╛ рдХреЛ рдХрд┐рд╕ рд╕рдВрд╡реИрдзрд╛рдирд┐рдХ рд╕рдВрд╢реЛрдзрди рджреНрд╡рд╛рд░рд╛ рд╕рдВрд╡рд┐рдзрд╛рди рдХреА рдЖрдая┐╜...
рдЗрдирдореЗ рд╕реЗ рдХреНрдпрд╛ тАШMutualтАЩ рдХрд╛ рд╕рд╣реА рдЕрд░реНрде рдирд╣реА рд╣реИ?
┬ардирд┐рдореНрдирд▓рд┐рдЦрд┐рдд рдореЗрдВ рд╕реЗ рдХреМрди рд╕рд╛ тАШAnticipated increase рд╢рдмреНрдж рдХрд╛ рд╡рд┐рддреНрддреАрдп рд╢рдмреНрджрд╛рд╡я┐╜...