If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is the possible value of (a + b + c)?

585

a    :    b    :    c

3    :    4    :   __

__  :    2    :    1

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*Note: Fill the numbers in the blanks, which is immediately left or right to the given numbers in a row.

We get:

a    :    b    :    c

3    :    4    :    4       ..........(i)

2    :    2    :    1       ..........(ii)

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6    :    8    :    4              (product of (i) & (ii))

3    :    4    :   2    = 9R

Now,     

a + b + c = 9R

So, the value must be a multiple of 9

Out of all options, (c) satisfies i.e. 585