The price of a ring varies jointly with the cube root of no. of diamonds and
weights of gold used in it, the price
of the king was 10000, when it has
64 diamonds 15gm. of gold
find the no. of diamonds if the price of
ring was 10500 weight of gold was
21 gm. ?​

d = 27

Step-by-step explanation:

Let price = p

Number of diamonds = d

Weigh of gold = w

Hence,

P α d^1/3w

P = kd^1/3 * w

k = proportionality constant

P = 10000 ; d = 64 ; w = 15

We can obtain the value of k

10000 = k * 64^1/3 * 15

10000 = k * 4 * 15

10000 = 60k

k = 10000 / 60

Hence,

P = (10000/60)*d^(1/3)*g

To find the number of d ; when P = 10500 ; g = 21

10500 = (10000/60)*d^1/3 * 21

10500 = 3500 * d^1/3

10500 / 3500 = d^1/3

3 = d^1/3

3³ = d

27 = d