I bought a certain number of marbles at a rate of 27 marbles for rupees 2 times M,where M is an integer.I divided these marbles into 2 parts of equal numbers,one part of which I sold at the rate of 13 marbles for RS M and the other at the rate of 14 marbles for Rs M.I spent and received an integral no of rupees,but bought the least number of marbles.How many did I buy?

• Let he bought x marbles.
  27 marbles costs = Rs. 2M
  Therefore, x marbles costs = Rs. (2M * x) / 27
  Since the marble is divided into 2 equal parts so the number x should be an even number.
  For first x/2 marbles,
  13 marbles s.p. is = Rs. M
  Therefore, x/2 marbles s.p. = Rs. (M * x) / 26
  For other x/2 marbles,
  14 marbles s.p. is = Rs. M
  Therefore, x/2 marbles s.p. = Rs. (M * x) / 28
  Now we can't equate like [(M * x) / 26] + [(M * x) / 28] = (2M * x) / 27
  because (M *x ) will get cancel each side and of course 1/28 + 1/26 is not equal to 2/27
  So here we don't need M and we can cancel it. After that we have,
  CP = 2x/27
  For first x/2 marbles,
  SP = x/26
  And for other x/2 marbles,
  SP = x/28
  Now this CP and SP must be an integer (as per question). So we have to find a number x which will be divisible simultaneously by 27, 26 and 28. So we have to find the LCM of 26, 27, 28 which will turn out minimum value as 9828 and it is even as well. So the value of x will be 9828 minimum.
• 8 years agoHelpfull: Yes(17) No(1)
• this is an easy question. answer is a)9828
• 9 years agoHelpfull: Yes(6) No(25)
• please explain clearly....
• 9 years agoHelpfull: Yes(4) No(0)
• can any1 plz explain
  
• 9 years agoHelpfull: Yes(2) No(0)
• least no of marbles=27*2=54
  
• 9 years agoHelpfull: Yes(2) No(5)
• Answer: d
  
  Explanation:
  
  Let he bought 2x marbles.
  
  27 marbles costs = Rs.2M so 1 marble costs = Rs.2M/27
  
  Therefore, x marbles costs = Rs. (2M × x) / 27
  
  Now we calculate the selling prices.
  
  He sold x marbles at the rate of 13 for Rs.M so 1 marble selling price = M/13
  
  x marbles selling price = x × M/13
  
  He sold another x marbles at the rate of 14 for Rs.M so 1 marble selling price = M/14
  
  x marbles selling price = x × M/14
  
  Now 2Mx27,xM13,xM14 are integers.
  
  So x marbles must be divisible by 27, 13, 14.  LCM of 4914
  
  So 2x = 9828
• 8 years agoHelpfull: Yes(2) No(0)
• can u exaplain the solution . .
• 9 years agoHelpfull: Yes(1) No(0)
• rate is given 27 marbles for rs. 2M
  so 1 marble costs 2M/27
  suppose i have bought x marbles...so c.p =x*2M/27
  divide into 2 equal x/2 parts
  now 1st part sold at 13 marbles for M, so s.p of 1st part= x/2*M/13 and s.p of 2nd part is x/2*M/14
  as no profit or loss recieved..
  c.p=s.p
  x*2M/27 = x/2*M/13 + x/2*M/14
  we can take x and M common..and cancel them...so answr can be solved according to options only.
  correct me if i am wrong.
• 9 years agoHelpfull: Yes(1) No(5)
• 13*14+14*13=264
• 8 years agoHelpfull: Yes(1) No(2)
• cn any1 provide the solution.....?
• 9 years agoHelpfull: Yes(0) No(0)
• can u explain me @prashant gupta
• 9 years agoHelpfull: Yes(0) No(0)
• as marbles r least
  so my ans is 4
• 9 years agoHelpfull: Yes(0) No(0)
• plzz explain..
  
• 9 years agoHelpfull: Yes(0) No(0)
• this is least no.364
• 9 years agoHelpfull: Yes(0) No(1)
• number of marbles is equal to 27 bcoz here in QU it is mention that he bought min no of marbles.
• 9 years agoHelpfull: Yes(0) No(0)
• is it 364??
• 9 years agoHelpfull: Yes(0) No(1)
• 364 is not in option...so answer may be 9828 which was in option
• 9 years agoHelpfull: Yes(0) No(0)
• write it properly or dont write it. -_-
• 8 years agoHelpfull: Yes(0) No(0)