Of the three numbers, the ratio 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 numbers is $2400$ , then what is the second number?

45

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38

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22

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None of these

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Solution

The correct option is A $45$
Let the first and the second number be $8 x$ and $9 x$ respectively.
Given $9 x : T h i r d N u m b e r = 3 : 4$
$\Rightarrow \frac{9 x}{T h i r d N u m b e r} = \frac{3}{4} \Rightarrow T h i r d N u m b e r = \frac{9 x \times 4}{3} = 12 x$

Given $8 x \times 12 x = 2400$
$\Rightarrow x^{2} = \frac{2400}{96} = 25 \Rightarrow x = 5$
$∴$ Second number $= 9 \times 5 = 45$ .

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Of the three numbers, the ratio 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 numbers is 2400, then what is the second number?

The correct option is A 45Let the first and the second number be 8x and 9x respectively. Given 9x:ThirdNumber=3:4 ⇒9xThirdNumber=34⇒ThirdNumber=9x×43=12x Given 8x×12x=2400 ⇒x2=240096=25⇒x=5 ∴ Second number =9×5=45.

Of the three numbers, the ratio 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 numbers is $2400$ , then what is the second number?