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Price of a diamond is proportional to the square of its mass which is measured in carat. Let 6 carat diamond piece be divided into two pieces. After division the total price of the two pieces is 5/8 of the original price. Determine the mass of the pieces.

Price of a diamond is proportional to the square of its mass which is measured in carat. Let 6 carat diamond piece be divided into two pieces. After division the total price of the two pieces is 5/8 of the original price. Determine the mass of the pieces. Correct Answer 4.5 and 1.5

Given:

Price of diamond ∝ square of mass

Calculation:

Let price of diamond be p and mass in carat be m

p ∝ m2 or p = km2 ----- (1)

Original mass = 6 carats

Original price = k × 36 = 36k            From (1)

Let the mass of two pieces be x and 6 – x

Price of 1st piece = kx2

Price of 2nd piece = k(6 – x)2 = k (36 + x2 – 12x)

Total price of broken pieces = (5/8) × 36k = 45k/2

45k/2 = k (36 + x2 – 12x) + kx2

45 = 4x2 + 72 – 24x

4x2 – 24x + 27 = 0

4x2 – 18x – 6x + 27 = 0

2x (2x – 9) – 3 (2x – 9) = 0

x = 4.5 or 1.5

∴ The weights are 4.5 carats and 1.5 carats.

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