High School

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Due to a reduction of [tex]6 \frac{1}{4}[/tex] in the price of wheat, a man can buy 1 kg more for 135. Find the original rate of wheat per kg.

Answer :

The original rate of wheat per kg is calculated as 34.375 units. This is derived using a quadratic equation based on the given reduction in price and additional quantity obtained.

  • The quantity bought at the original price: 135/x
  1. At the reduced price, he can buy: 135/(x - 6.25)
  2. The difference in quantity is 1 kg:

135/(x - 6.25) - 135/x = 1

To solve this equation, multiply through by x(x - 6.25) to get rid of the denominators:

135x - 135(x - 6.25) = x(x - 6.25)

Simplifying, we get:

135 * 6.25 = x(x - 6.25)

840.625 = x² - 6.25x

Rearranging into a standard quadratic equation format:

x² - 6.25x - 840.625 = 0

Solving this quadratic equation using the quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a, where a = 1, b = -6.25, and c = -840.625:

x = [6.25 ± sqrt((6.25)² + 4*840.625)] / 2

x = [6.25 ± sqrt(3906.25)] / 2

x = [6.25 ± 62.5] / 2

This provides two possible solutions:

x₁ = (6.25 + 62.5) / 2 = 34.375

x₂ = (6.25 - 62.5) / 2 = -28.125 (not feasible as price can't be negative)

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Rewritten by : Barada