Multiple choice

If a, b, c are three sums of money such that b is the simple interest on a, c is the simple interest on b for the same time and at the same rate of interest, then we have

  1. $a^2 = bc$
  2. $b^2 = ac$
  3. $C^2 = ab$
  4. $abc = 1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

b = a*r*t/100. c = b*r*t/100. Let k = rt/100. b = ak, c = bk. c = (ak)k = ak^2. Also ac = a(ak^2) = a^2k^2 = (ak)^2 = b^2.

AI explanation

Since b is the simple interest on a and c is the simple interest on b for the same time and rate, we have b = (a * r * t)/100 and c = (b * r * t)/100. Multiplying these two equations gives b * c = (a * b * r^2 * t^2) / 10000. Dividing both sides by b yields c = (a * r^2 * t^2) / 10000. Substituting (r * t / 100) = b/a from the first equation into this gives c = a * (b/a)^2, which simplifies to c = b^2/a. Rearranging this relation shows b^2 = ac.

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