the sum of three numbers is 98 if the ratio first..., Ratio & Proportion, General Mathematics

Question:The sum of three numbers is `98`. If the ratio of the first to the second is `2 : 3` and that of second to the third is `5 : 8`, then the second number is :

A `20` 
B `30` 
C `48` 
D `58`

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+ AnswerB

+ ExplanationLet the numbers be `A, B` and `C`.

Then, `A : B = 2 : 3` and 

`B : C = 5 : 8`

`= 3/5 xx 5 : 3/5 xx 8`

`= 3 : (24)/5`.

`:. A : B : C = 2 : 3 : (24)/5`

`= 10 : 15 : 24`.

Second number `= (98 xx (15)/(49))`

`= 30`.

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