the delegates of only five countries

[sanju09]

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


Made Up!

[mathrupradeep]

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]

[theCodeToGMAT]

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]

[GMATGuruNY]

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.