Some people are standing square. From them 32 are removed and then form a small square and
then 8 more removed. now we cannot form the square. so how many people are there at the
beginning?

• 81
  
  We should find the two square numbers whose difference is 32. Starting from 9,16,25,36,49,64,81,100,....
  We observe 81-49=32 & 49-8=41 which is not a square.
• 9 years agoHelpfull: Yes(18) No(13)
• If we take each side 10students,then it will be 40 and when we remove 32 we have only 8 students means each side 2 will be there, if we remove 8 too then there is no square to form.
• 9 years agoHelpfull: Yes(6) No(3)
• for such questions always try to cross check the options.
  let initially x^2 people were standing in the square and after removal of 32 people from this new square becomes y^2. therefore x^2-32=y^2 or x^2-y^2=32 or (x+y)(x-y)=32
  but 32=1*32 or 2*16 or 4*8 so (x+y)(x-y)= 1*32 or 2*16 or 4*8
  now x+y= 32 or 16 or 8
  x-y= 1 or 2 or 4
  find the solution in each case and check which one of these satisfies the condition. the one which satisfies all the condition given in the question is answer.
• 9 years agoHelpfull: Yes(1) No(1)
• correct explanation plzz....
• 9 years agoHelpfull: Yes(0) No(0)
• no solution
• 8 years agoHelpfull: Yes(0) No(0)
• Ans : 40
  Explanation :
  
  Let n be the initial number of people.
  These n people form a square.
  Now 32 people are removed.
  Therefore now number of people = n - 32.
  Now again 8 people are removed from n - 32 people => now people remained = n - 40.
  Now we cannot form a square with these n - 40 people.
  Here we cannot forming a square means that no of people = 0
  i.e, n - 40 = 0
  so n = 40.
  Thus initial number of people = 40.
• 7 years agoHelpfull: Yes(0) No(0)
• 9,16,25,36,49,64,81
  49=49-32-8= 9 which is square
  64=64-32-8=24.which is not square
• 7 years agoHelpfull: Yes(0) No(0)