Discussion
What number should be subtracted from each of 50, 61, 92, 117 so that the numbers, so obtained in this order, are in proportion ?
Answer: B
The number to subtract is 17.
If x is subtracted, (50 − x) : (61 − x) = (92 − x) : (117 − x). The product of the extremes equals the product of the means:
\[ \begin{aligned} (50 - x)(117 - x) &= (61 - x)(92 - x) \\ 5850 - 167x &= 5612 - 153x \\ 238 &= 14x \\ x &= 17 \end{aligned} \]
Check: 33, 44, 75, 100, and 33 : 44 = 3 : 4 = 75 : 100. Subtracting 14, 19 or 23 does not give equal ratios (for example 14 gives 36 : 47 and 78 : 103).
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