Question : Of three positive numbers, the ratio of 1st and 2nd is 8 : 9, and that of 2nd and 3rd is 3 : 4. The product of 1st and 3rd is 2400. The sum of the three numbers is:
Option 1: $45$
Option 2: $85$
Option 3: $95$
Option 4: $55$
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Correct Answer: $45$
Solution : Let the first and the second numbers be $8x$ and $9x$. Given, Second Number : Third Number = $3 : 4$ $\frac{9x}{\text{Third number}} = \frac{3}{4}$ So, the third number = $12x$ The product of the first and third numbers is 2400. $8x×12x = 2400$ or, $x^2 = 25$ or, $x = 5$ Second number = $9x = 9 × 5 = 45$ Hence, the correct answer is $45$.
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