The price of a diamond is proportional to the square of its weight. If the price of a diamond weighing $5$ carat is Rs. $25$ , find the price of another diamond weighing $1$ carat.

Open in App

Solution

Let price be denoted by $p$ and weight by w
$\Rightarrow p \propto w^{2} \Rightarrow \frac{p_{1}}{p_{2}} = \frac{w_{1}^{2}}{w_{2}^{2}}$
$\Rightarrow p_{2} = p_{1} \times \frac{w_{2}^{2}}{w_{1}^{2}}$
$\Rightarrow p_{2} = 25 \times {(\frac{1}{5})}^{2} = \frac{25}{25} = R s . 1$ .

Suggest Corrections

Similar questions

Q. The price of a diamond varies as the square of its weight. Three rings of equal weight, each composed of a diamond set in gold, have values pounds

a, b, c

, the diamond in them weighing

3, 4, 5

carats respectively. Show that the value of a diamond of one carat is
pounds

(\frac{a + c}{2} - b)

,
the cost of workmanship being the same for each ring.

The price of a diamond is proportional to the square of its weight. The diamond accidentally fell and broke into four pieces whose weights are in the ratio of 1 : 2 : 3 : 4. If the price fetched is Rs. 70,000 less than the original price, find the original price.

Q. A diamond price is proportional to square of its weight it gets broken onto

4

pices with its weight in the ratio

1 : 2 : 3 : 4

. The total price of diamond after breaking is

70000

less than the diamond in original.What was the price of the original diamond?

Q. Price of a piece of diamond is Rs. 2000. It is broken into two equal pieces. If price of diamond is directly proportional to the square of its weight, then the amount of loss for breaking into two pieces is

Q. Weighing 3104 carats (1 carat = 200 mg), the Cullinan diamond was the largest natural diamond ever found How many carbon atoms were present in the stone?

Join BYJU'S Learning Program

The price of a diamond is proportional to the square of its weight. If the price of a diamond weighing 5 carat is Rs. 25, find the price of another diamond weighing 1 carat.

Let price be denoted by p and weight by w⇒p∝w2⇒p1p2=w21w22⇒p2=p1×w22w21⇒p2=25×(15)2=2525=Rs.1.

The price of a diamond is proportional to the square of its weight. If the price of a diamond weighing $5$ carat is Rs. $25$ , find the price of another diamond weighing $1$ carat.

Let price be denoted by $p$ and weight by w
$\Rightarrow p \propto w^{2} \Rightarrow \frac{p_{1}}{p_{2}} = \frac{w_{1}^{2}}{w_{2}^{2}}$
$\Rightarrow p_{2} = p_{1} \times \frac{w_{2}^{2}}{w_{1}^{2}}$
$\Rightarrow p_{2} = 25 \times {(\frac{1}{5})}^{2} = \frac{25}{25} = R s . 1$ .