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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
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B
20
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C
30
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D
32
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E
33
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Solution

The correct option is C 30
Let 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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