A thief steals four gallons of liquid soap kept in a train compartment’s bathroom from a container
that is full of liquid soap. He then fills it with water to avoid detection. Unable to resist the
temptation he steals 4 gallons of the mixture again, and fills it with water. When the liquid soap is
checked at a station it is found that the ratio of the liquid soap now left in the container to that of
the water in it is 36 : 13. What was the initial amount of the liquid soap in the container if it is
known that the liquid soap is neither used nor augmented by anybody else during the entire
period?

• Let total quantity = x gallons;
  4 gallons are drown out 2 times;
  let y = 4 and n = 2;
  
  By formula.....{x(1-y/x)^n}/x=36/36+13;
  =>solving we get (1-4/x)^2=36/49;
  =>(x-4)/x=6/7;
  =>x=28 ans.
• 7 years agoHelpfull: Yes(3) No(1)
• let x be gallons, step 1 soap=x-4, water=4
  step soap=x-4-4*(x-4)/x water=4+4-4*4/x;
  soap/water=36:13
  calculate x
  x=28
• 7 years agoHelpfull: Yes(2) No(2)
• simple method:
  first calculate liquid percentage in remaining solution i e 36/49*100 =73.5% liquid remaining in solution
  
  let 100l intial soln
  100%----------------------------- 73.5%(FINAL)
  14.5% -> 85.5%----->;
  14.5 % gives 73.5 approx(two times removed)
  hence 14.5% is 4 L(because removed liquid is 4L )
  100% ?
  gives 28 approx
  
  we have to choose random % taken out and try
• 7 years agoHelpfull: Yes(1) No(2)
• 1st time - soap/mixture = (V-4)/V
  2nd time - soap/mixutre =(V-4)^2/V^2 = 36/(36+13)
  Solving this V= 28
• 7 years agoHelpfull: Yes(1) No(4)
• 64.3 gallons
• 7 years agoHelpfull: Yes(0) No(6)
• Remember this formula for questions like these:
  
  Amount of item / Total amount = (1 - (amount replaced / original amount)) ^ 2
  
  According to this, the answer is:
  
  36 / (36 + 13) = (1 - (4 / x)) ^ 2
  
  Solving, we get x = 28
• 4 years agoHelpfull: Yes(0) No(0)