Question

The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4800. Find the cost of a diamond (in rupees) of the same kind weighing 8 decigrams.

Answer 1

Hint: Formulate the equation relating the cost of the diamond and its weight according to the relation given in the question. Find the unknown parameter in the equation using the given values in the diamond. The cost of the diamond can then be calculated for 8 decigrams of weight.

Complete step-by-step answer:
We are given that the cost of the diamond varies proportional to the weight of the diamond, therefore we can say that $C$ is proportional to ${w^2}$ where $C$ is the cost of the diamond in rupees and $w$ is the weight of the diamond in decigrams.
We can formulate an equation relating the cost of the diamond and the weight of the diamond by introducing a constant of proportionality, say $k$.
Thus , $C = k{w^2}$ where $k$ is the constant of proportionality.
We are given that 20 decigrams of diamond cost Rs. 4800, therefore substituting 4800 for $C$ and 20 for $w$, we get
$4800 = k{\left( {20} \right)^2}$
We can solve the above equation to find the value of $k$
$4800 = 400k$
Dividing the equation by 400, we get
$k = 12$
Substituting the value 12 for $k$ in the equation $C = k{w^2}$, we get
$C = 12{w^2}$
To find the cost of 8 decigrams of diamond, substitute the value 8 for w in the equation $C = 12{w^2}$
$C = 12{\left( 8 \right)^2}$
$C = 768$
Thus the cost of 8 decigrams of diamond is Rs. 768.

Note: The formulation of the equation relating the cost of the diamond and its weight must be according to the relation specified in the question. The dimensions of the various variables must be kept the same throughout the solution process.