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Correct Answer: 10

Because, x/2+y/3=4

= 3x+2y/6=4

= 3x+2y=24 …(i)

and 2/x+3/y=1=2y+3x/xy=1

= 2y+3x=xy …(ii)

From Eqs. (i) and (ii),

xy = 24

There are 6 possibilities for x and y, respectively.

2 *12, 3*8,4*6, 6*4,8*3,12*2

2 and 12 cannot be the values of x and y as their sum is 14 and it is not given in options.

Now, we check both 3 and 8 as well as 4 and 6 as values of x and y or value of y and x.

Only 4 as a value of x and 6 as a value of

y satisfied the given condition x/2+y/3=4.

So, x=4 and y=6

Therefore, x+y=4+6=10