:: - Discussion

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Explanation:
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.