A sum is divided among A, B, C and D such that the ratio of the shares of A and B is 1 : 3, that of B and C is 1 : 4 and that of C and D is 3 : 4. If the difference between the shares of A and D is Rs 630, then the sum is :

1344

a    :    b    :    c    :    d

1    :    3    :   __   :   __

__  :    1    :    4    :   __

__  :   __   :    3    :    4

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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    :    d

1    :    3    :    3    :    3       ..........(i)

1    :    1    :    4    :    4       ..........(ii)

3    :    3    :    3    :    4       ..........(iii)

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3    :    9     :   36   :  48              (product of (i) to (iii))

1    :    3     :   12   :   16     =  32R (total)

Now,

Difference between A & D = 15R = 630

⇒ 1R = 42

Hence, Sum = 32R = 32 x 42 = 1344