Question

The cost of diamond varies directly as the cube of its weight. Once this diamond broke into 4 pieces with weights in the ratio 3 : 2 : 1 : 1. When the pieces were sold the merchant got 30600 less. Find the original price of the diamond?
1. Rs. 35000
2. Rs. 46400
3. Rs. 36450
4. Rs. 34300

Answer 1

Correct Answer - Option 4 : Rs. 34300

Given:

Ratio of diamond when broke is 3 : 2 : 1 : 1.

When the pieces were sold the merchant got 34600 less.

Concept used:

Using the concept simple ratio.

Calculation:

Let the weight of each piece of diamond be 3x, 2x, x and x.

Total weight of diamond = 3x + 2x + x + x = 7x  

Cost of the diamond = (7x)³ = 343x³

Cost of first piece = (3x)³ = 27x³

Cost of second piece = (2x)³ = 8x³

Cost of third piece = (x)³ = x³

Cost of fourth piece = (x)³ = x³

Total cost of diamond after weight = 27x³ + 8x³ + x³ + x³

⇒ New cost = 37x³

According to the question,

343x³ – 37x³ = 30600

⇒ 306x³ = 30600

⇒ x³ = 100

So, the original cost of diamond = 343x³ = 343 × 100 = Rs. 34300

∴ The original cost of diamond is Rs. 34300.