Multiple choice

A student was asked to find the product of three real numbers π‘Ž, 𝑏 and c. He committed a mistake in copying all the three numbers and ended up in a result where the value of a got increased by 33β…“%, the product of a and b got increased by 20% and the product of π‘Ž,𝑏 and c got increased by 35%. Which of the following gives the percentage change in the value of c?

  1. 10%

  2. 12.5%

  3. 15%

  4. 16.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P = abc. New P' = 1.35P. New a' = 1.333a = (4/3)a. New (ab)' = 1.2ab. Since (ab)' = a'b', b' = 1.2ab / (4/3)a = 0.9b. Now P' = a'b'c' = 1.2ab * c' = 1.35abc. So c' = 1.35/1.2 * c = 1.125c. This is a 12.5% increase.

AI explanation

Let the original values be a, b and c, and the copied values be a', b' and c'. A 33.33% increase means a' is 4/3 of a, so b' must be 9/10 of b to make the product of a and b increase by 20% (since 4/3 * 9/10 = 1.2). To make the final product increase by 35%, c' must be 9/8 of c (since 1.35 / 1.20 = 1.125). The percentage change in the value of c is therefore 12.5%.

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