Question

A diamond is broken into three parts in the ratio 1 ∶ 2 ∶ 3. The price of diamond is in proportion to cube of its weight. If the price of diamond before broken is Rs. 47520, then find the loss in the price of diamond after broken.
1. Rs. 50000
2. Rs. 39600
3. Rs. 47400
4. Rs. 42000

Answer 1

Correct Answer - Option 2 : Rs. 39600

Given:

A diamond is broken into three parts in the ratio 1 ∶ 2 ∶ 3

The price of diamond before broken = Rs 47520

Concept:

In this type of questions we can calculate the actual weight of diamond by adding al the ratios.

Calculation:

Let the weight of 3 parts be x, 2x, and 3x

So actual weight of diamond = x + 2x + 3x = 6x

According to question

The price of diamond is in proportion to cube of its weight

The price of diamond before broken = (6x)³

⇒ 216x³

The price of diamond after broken = x³ + (2x)³ + (3x)³

⇒ x³ + 8x³ + 27x³

⇒ 36x³

The price of diamond before broken = 216x³

⇒ 216x³ = 47520

⇒ x³ = 220

Loss in the price after broken = 216x³ – 36x³

⇒ 180x³

⇒ 180 × 220

⇒ 39600

∴ The loss in the price of diamond after broken is Rs 39600.