Question

A diamond weighing 35 grams cost Rs. 12,250 is cut down into two pieces having weights in the ratio of 5 ∶ 2. If the price directly proportional to the square of the weight then find the loss incurred.
1. Rs. 5000
2. Rs. 6000
3. Rs. 5500
4. Rs. 5700

Answer 1

Correct Answer - Option 1 : Rs. 5000

Given:

New ratio is 5 ∶ 2.

The price of diamond before broken is Rs. 12250.

Concept used:

Using the concept simple ratio.

Calculation:

Let the weight of each piece of diamond be 5x and 2x.

Total weight of diamond = 5x + 2x = 7x   

Cost of the diamond = (7x)² = 49x²

Cost of first piece = (5x)² = 25x²

Cost of second piece = (2x)² = 4x²

Total cost of diamond after weight = 25x² + 4x² = 29x² 

⇒ New cost = 29x2 

According to the question,

49x² = 12250

⇒ x² = 250

The loss in the price of diamond after broken = 49x² – 29x²

⇒ The required loss = 20x²

⇒ 250 × 20

⇒ Rs. 5000

∴ The loss in the price of diamond after broken is Rs. 5000.