Question : In three positive numbers, the ratio of first and second is 3 : 4 and the ratio of second and third is 3 : 5. The product of first and third is 4500. What is the sum of the three numbers?
Option 1: 282
Option 2: 235
Option 3: 198
Option 4: 205
Correct Answer: 205
Solution :
The ratio of first and second = 3 : 4 = 9 : 12
The ratio of second and third = 3 : 5 = 12 : 20
The ratio of three numbers = 9: 12 : 20
Let the numbers be $9x$, $12x$, and $20x$.
Product of first and third = 4500
⇒ $9x×20x = 4500$
⇒ $x^2 = \frac{4500}{180}$ = 25
⇒ $x = 5$
The sum of the three numbers
$=9x+12x+20x$
$= 41x$
$= 41 × 5$
$= 205$
Hence, the correct answer is 205.
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