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From the given information about sales,
15x + 10y =125.
So, 3x + 2y = 25

Also, from the given information about profits
5x + 2y = 27 or 31 or 25 or 39 or 41.

Lets take the first case : 5x + 2y = 27.
Solve this and the earlier sales eqn, we get x = 1, y = 11. The values of x and y fit well in to both the equations.

Test this for each of the 5 possibilities of value of profit. Its fits for each except for 5x + 2y = 41. If we solve this and sales eqn, we get x = 8. But if we substitute, x = 8 in either of the eqn. y is not an integer. So the answer is E.