Question : The ratio of three numbers is 3 : 6 : 8. If their product is 9216, then what is the sum of the three numbers?
Option 1: 96
Option 2: 72
Option 3: 144
Option 4: 68
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Correct Answer: 68
Solution :
Given: The ratio of three numbers is 3 : 6 : 8.
Their product is 9216.
Let the numbers be $3k, 6k$, and $8k$.
Product of $3k × 6k × 8k = 9216$
⇒ $144k^{3}=9216$
⇒ $k^{3}=\frac{9216}{144}$
⇒ $k=\sqrt[3]{64}$
⇒ $k=4$
The sum of the numbers $=3k+ 6k+8k=17k= 17 × 4 = 68$
Hence, the correct answer is 68.
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