Question : Four numbers are in the ratio 1 : 2 : 3 : 5. Two times their sum is 44. Find the ratio in the numbers obtained by subtracting 3 from the cube of each number
Option 1: 2 : 31 : 204 : 999
Option 2: 3 : 13 : 208 : 992
Option 3: 11 : 67 : 219 : 1003
Option 4: 5 : 61 : 213 : 997
Correct Answer: 5 : 61 : 213 : 997
Solution : Let the numbers be $x$, $2x$, $3x$ and $5x$ respectively. According to the question, $⇒ 2(x + 2x + 3x + 5x) = 44$ $⇒ 11x = \frac{44}{2}$ $⇒ x = \frac{22}{11} = 2$ So, the numbers are 2, 4, 6 and 10 respectively. Cube of the numbers are 8, 64, 216, and 1000 Subtracting 3 from each term to get the required ratio$= 5 : 61 : 213 : 997$ Hence, the correct answer is 5 : 61 : 213 : 997.
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