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1. Of the three numbers, the ration of the first and the second is 8 : 9 and that of the second and third is 3 : 4. If the product of the first and third number is 2400. then the second number is = ?

A. 45

B. 40

C. 24

D. 10

Solution:

\begin{aligned} A : B : C \\ 8 : 9 \\ 3 : 4 \\ 8 : 9 : 12 \\ 8 x : 9 x : 12 x \\ ∴ 8 x \times 12 x = 2400 \\ \Rightarrow x^{2} = \frac{2400}{12 \times 8} \\ \Rightarrow x = 5 \\ ∴ B = 9 \times 5 = 45 \end{aligned}

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