IPMAT Indore 2023 · Quantitative Ability · Question 32

Step 1 — count the beads. Volume scales as the cube of the radius. Each bead has 1/5 the radius, so 1/125 the volume:

\text{number of beads}={5}^{3}=125

(The gold is conserved — melting changes shape, not volume.)

Step 2 — find the total selling price. A 20% profit on a cost of ₹10,00,000:

S{P}_{\text{total}}=1.2\times 1000000=1200000

Step 3 — selling price per bead.

S{P}_{\text{bead}}=\frac{1200000}{125}=9600

Step 4 — undo the discount. The beads sold at 20% off the listed price, so SP=0.8\times LP:

LP=\frac{9600}{0.8}=12000

Answer: Option 1 — ₹12,000

Shortcut. Three steps, each one multiplication:

LP=\frac{1000000\times 1.2}{125\times 0.8}=\frac{1200000}{100}=12000

Notice 125\times 0.8=100 exactly — the numbers were chosen to collapse.

Option 3 (9600) is the planted trap: that is the selling price per bead, the value you reach one step before the end. Discount is always applied to the listed price, so you divide by 0.8 rather than multiplying. Options 2 and 4 come from using {5}^{2} or {5}^{1} beads instead of {5}^{3}.