[30] The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second t

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

Explanation:

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = $(5 \times\dfrac{3}{5}) : (8 \times\dfrac{3}{5}) = 3 : \dfrac{24}{5}$

=> A : B : C = 2 : 3 : $\dfrac{24}{5}$ = 10 : 15 : 24

=> B = $(98 \times \dfrac{15}{49}) = 30$
=> B = 30

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