Question

A certain bag contains only red balls, green balls, and blue balls and no other balls. The ratio of the number of red balls to the number of blue balls is 2:3, and the ratio of the number of blue balls to the number of green balls is 4:3. The number of blue balls in the bag is what fraction of the total number of balls in the bag?

A.
`(3)/(8)`
B.
`(12)/(29)`
C.
`(7)/(13)`
D.
`(15)/(23)`
E.
`(12)/(17)`

Answer 1

Option B is right

Explanation:

Given that a certain bag contains only red balls, green balls, and blue balls and no other balls. The ratio of the number of red balls to the number of blue balls is 2:3, and the ratio of the number of blue balls to the number of green balls is 4:3.

Red balls = 2x means blue balls = 3x

if blue balls = 3x then green balls would be =
`(3x(3))/(4) \\2.25x`

Now converting everything in terms of y we have

no of red balls = 2x, blue balls = 3x and green balls = 2.25x

Total balls = 7.25x

No of blue balls to total balls =
`(3x)/(7.25x) \\=(12)/(29)`

Thus we find that option B is the only right answer