C:F:I is 12:15:8 -- (1)
R:A:C is 5:4:6 -- multiply by 2

R:A:C is 10:8:12 -- (2)

combining (1) and (2)

R:A:C:F:I
10:8:12:15:8

given that R=I+6
R/I=10/8

so I =24

and 8x=24.. so x=3.

adding all the rations we get

10+8+12+15+8=53

53x=159

so the answer is E[/b][/b]

C:F:I = 12:15:8
R:A:C: = 5:4:6
R = I + 6

To find: Total number of delegates

Let total be "x"
Multiply the ratio of RAC by 2
So, R : A : C = 10 : 8 : 12

Now, R : A : C : F : I = 10 : 8 : 12 : 15 : 8

R = 10/53 * x
I = 8/53* x

So,
10x = 8x + 53*6
x = 53*3 = 159

[spoiler]{E}?[/spoiler]

sanju09 wrote:In an International summit where the delegates of only five countries are the attendees, the ratio in Canadian to French to Indian delegates is 12:15:8, and the ratio in Russian to American to Canadian delegates is 5:4:6. If there are 6 more Russian delegates than the Indian delegates attending the summit, what is the total number of delegates attending the summit?
A. 44
B. 50
C. 53
D. 106
E. 159

C : F : I = 12:15:8.
R : A : C = 5:4:6 = 10:8:12.
Combining the ratios, we get:
R : A : C : F : I = 10:8:12:15:8.

In the resulting ratio:
Sum of the parts = 10+8+12+15+8 = 53.
R-I = 10-8 = 2.

Since the problem states that the difference between the number of Russian delegates and the number of Indian delegates is 6 -- 3 times as great -- all of the values in the ratio must be multiplied by a factor of 3.
Thus, the sum of the parts -- which represents the TOTAL NUMBER OF DELEGATES -- must also be multiplied by a factor of 3:
3*53 = 159.

The correct answer is E.