The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond of the same kind weighing 8 decigrams.

768

Step-by-step explanation:

let C represent cost and w weight, then the equation relating them is

C = kw² ← k is the constant of variation

To find k use the condition w = 20, C = 4800, that is

4800 = k * 20² = 400k (divide both sides by 400)

12 = k

C = 12w² ← equation of variation

When w = 8, then

C = 12 * 8² = 12 * 64 = 768