Please explain the solution, opts are 48 ltrs, 36 ltrs , 24 ltrs , 16 ltrs.

There are 10 filling pipes each capable of filling a cistern alone in 6 minutes and 6 emptying pipes each capable of emptying a cistern alone in 8 minutes. All pipes are opened together and as a result, tank fills 22 litres of water per minute. Find the capacity of the tank.

12 Answers
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12 Answers
Top Voted Recent Answer
  • Solution is here Let the capacity of cistern be 'x' ltrs Let's Talk about filling pipes Each filling pipe can fill the cistern in 6 min = x ltrs It's 1 min work = x/6 ltrs So 10 filling pipes 1min work = 10x/6 ltrs Now talk about emptying pipes Each emptying pipe can empty the cistern in 8 min = x ltrs Each emptying pipe 1min work = -x/8 ltrs 6 emptying pipes 1 min work = -6x/8 ltrs All pipes are open so 10x/6 - 6x/8 = 22 ltrs From solving above equation we will get the value of x = 24 ltrs which is the capacity of the tank.
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  • 24
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  • Solution is here Let the capacity of cistern be 'x' ltrs Let's Talk about filling pipes Each filling pipe can fill the cistern in 6 min = x ltrs It's 1 min work = x/6 ltrs So 10 filling pipes 1min work = 10x/6 ltrs Now talk about emptying pipes Each emptying pipe can empty the cistern in 8 min = x ltrs Each emptying pipe 1min work = -x/8 ltrs 6 emptying pipes 1 min work = -6x/8 ltrs All pipes are open so 10x/6 - 6x/8 = 22 ltrs From solving above equation we will get the value of x = 24 ltrs which is the capacity of the tank. Hope you guys understand well Thankyou
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  • 24 Liters
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  • 24 Ltrs
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  • 24 
    -> first calculate for 1 min , the amount of water a filling pipe can fill , assuming that the total          capacity of the tank to be variable 'x' => for 1 min a filling pipe can fill x/6 of the tank.
    BUT there are 10 such pipes => total amount of water filled in 1 min is 10*(x/6)

    -> use the same logic for the emptying pipes => in 1 min the total amount of water cumilatively emptied by the pipes = 6*(x/8)

    -> water filled in 1 min is given as 22 => {10*(x/6)} -  { 6*(x/8)} =22 
    Solve for x and its value will be 24
     
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  • let tank capacity be x litres.A filling tap fill it in 6 minutes ,so in 1minute it fills x/6 and emptying pipe empty in 8 minutes so in 1 minute x/8 and given 10 filling pipes and 6 emptying pipes so in 1 minute 10x/6-6x/8=22(given), on solving for x we get 24.
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  • Work done in one minute by 10 pipes filling and 6 pipes emptying the cistern is
        10(1/6)-6(1/8) = 11/12
    Time = 1/work ==> Time = 12/11 * 22 = 24 ltrs.

    the answer is 24 ltrs.
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