Multiple choice

A jeweller purchased a large gemstone in the shape of a sphere at a cost of INR 8,00,280. The jeweller then decided to cut the gemstone into smaller spherical pieces, each with a radius one-sixth of the radius of the original gemstone, for sale. Assuming negligible cost for cutting, if the jeweller sold all the pieces of gemstones at a 25% discount on the marked price and made a total profit of 20%, what was the marked price of each piece of gemstone in INR?

  1. 2,598

  2. 5,928

  3. 8,952

  4. 9,825
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere is proportional to r^3. Cutting into pieces with r/6 means each piece has volume (1/6)^3 = 1/216 of the original. Total pieces = 216. Profit 20% on 800,280 = 960,336 total revenue. Revenue per piece = 960,336 / 216 = 4,446. Selling price = 0.75 * Marked Price = 4,446. Marked Price = 4,446 / 0.75 = 5,928.

AI explanation

When a sphere is cut into smaller spheres with one-sixth of the original radius, the total volume divides into six cubed pieces, yielding 216 smaller gemstones. The total cost price for all pieces is INR 8,00,280, and a 20% profit means the total selling price is 1.2 times 8,00,280, equaling INR 9,60,336. Since these pieces were sold at a 25% discount on the marked price, the total marked price is 9,60,336 divided by 0.75, resulting in INR 12,80,448. Dividing this total marked price by 216 pieces gives the marked price of each piece as INR 5,928.

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