Multiple choice

A goldsmith bought a large solid golden ball at INR 10,00,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price of each golden bead, in INR, was

  1. 12,000

  2. 24,000

  3. 9,600

  4. 48,000
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A Correct answer
Explanation

Volume of large ball = V. Volume of one bead = (1/5)^3 * V = V/125. Number of beads = 125. Total cost = 10,00,000. Profit = 20%, so total revenue = 12,00,000. Selling price per bead = 12,00,000 / 125 = 9600. Since 9600 is after 20% discount, list price = 9600 / 0.8 = 12000.

AI explanation

The large golden ball is divided into smaller beads with radii one-fifth of the original, meaning the volume of each bead is 1 / 125 of the original ball. Dividing the total volume by the volume of one bead yields 125 beads. To make a 20% profit on his cost of INR 10,00,000, his total revenue must be 10,00,000 * 1.2 = INR 12,00,000. Since he sells all 125 beads at a 20% discount on the listed price, the total listed price for all beads is 12,00,000 / (1 - 0.20) = INR 15,00,000. Dividing this total listed price by 125 beads gives the listed price of each bead as 15,00,000 / 125 = INR 12,000.

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