Multiple choice general knowledge math & puzzles

Two numbers are such that their difference, their sum and their product are in ratio of 1:7:24. The product of the number is _______ ?

  1. 12

  2. 24

  3. 36

  4. 48
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the numbers be $x$ and $y$. $(y-x):(y+x):xy = 1:7:24$. From $(y-x)/(y+x) = 1/7$, we get $7y-7x = y+x$, so $6y=8x$ or $y=4x/3$. Substituting into $(y+x)/xy = 7/24$ gives $(7x/3) / (4x^2/3) = 7/24$, which simplifies to $1/4x = 1/24$, so $x=6$. Then $y=8$. Product $xy = 48$.

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