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 after broken the loss of Rs. 39600 in the price, then find the price of diamond before broken.

1. Rs. 50000
2. Rs. 57420
3. Rs. 74250
4. Rs. 47520

Answer 1

Correct Answer - Option 4 : Rs. 47520

Given:

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

Loss after broken = Rs. 39600

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

Loss after broken = 216x³ – 36x³

⇒ 39600 = 180x³

⇒ x³ = 220

The price of diamond before broken = 216x³

= 216 × 220

= 47520

∴ The price of diamond before broken is Rs. 47520.