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: $55$
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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