Question

# The sum of three numbers is 98. The ratio of the first to the second is 2/3 and the ratio of the second to the third is 5/8. The second number is:

A
15
B
20
C
30
D
32
E
33

Solution

## The correct option is C 30Let a, b, c be the three numbers.$$a+b+c=98\\ \cfrac { a }{ b } =\cfrac { 2 }{ 3 } ,\cfrac { b }{ c } =\cfrac { 5 }{ 8 } \\ a=\cfrac { 2b }{ 3 } ,c=\cfrac { 8b }{ 5 } \\ \Longrightarrow \cfrac { 2b }{ 3 } +b+\cfrac { 8b }{ 5 } =98\Longrightarrow \cfrac { 49 }{ 15 } b=98\\ \therefore b=30$$Mathematics

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