Question

The value of certain rare diamonds varies directly with the cube of its weight. During transportation, the diamond broke into three pieces and the ratio of weights of these three pieces is 2 ∶ 2 ∶ 6.  A loss of 384 lacs was caused due to the breakage. The original price of the diamond is ______.
1. 0.7 crores
2. 5 crores
3. 10 crores
4. Data insufficient
5.

Answer 1

Correct Answer - Option 2 : 5 crores

Given:

Value of diamond ∝ (Weight of Cube)³

Ratio of weights of broken pieces = 2 ∶ 2 ∶ 6

Loss caused due to the breakage = 384 lacs

Calculations:

Let the weights of the broken pieces be 1, 1 and 3 (simplified) 

Original weight = 1 + 1 + 3

⇒ 5 units

Original price of diamond = k × 5³

⇒ 125 × k

Reduced price of diamond = k × (1³ + 1³ + 3³) 

⇒ 29 × k

Loss caused due to breakage = 96 × k

⇒ 96 × k = 384

⇒ k = 4

Original price of diamond = 125 × 4 

⇒ 500 lacs

∴ The original price of diamond is 500 lacs or 5 crores