Question : Three numbers are in the ratio of 1 : 2 : 3. The product of the three numbers is 1296. What is the sum of the three numbers?
Option 1: 36
Option 2: 30
Option 3: 72
Option 4: 24
Correct Answer: 36
Solution :
The ratio of three numbers = 1 : 2 : 3
Product of three numbers = 1296
Let the numbers be $x, 2x$ and $3x$.
Product of three numbers $= x × 2x × 3x = 6x^3$
So, 6x$^3$ = 1296
⇒ $x^3 = \frac{1296}{6} = 216$
⇒ $x = 6$
So, First number $= x = 6$
Second Number $= 2x = 2 × 6 = 12$
Third Number $= 3x = 3 × 6 = 18$
So, the sum of all numbers = 6 + 12 + 18 = 36
Hence, the correct answer is 36.
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