A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price of each golden bead, in INR, was

We are told that the radius of the small bead is 1/5th of the actual ball.

Let us assume that the radius of the initial sphere is r, the radius of the small bead will be r/5.

Number of small beads = $$\frac{\left(\frac{4}{3}\pi r^3\right)}{\frac{4}{3}\pi\frac{\ r^3}{125}}=125$$

So, the cost price of each bead = $$\frac{1000000}{125}=8000$$

We are told that he got a profit of 20%. So, the selling price should be 1.2*8000 = 9600.

And the selling price is after giving 205 discount. So, the marked price 0.8 MP=9600

 MP = 12000