IPMAT Indore 2022 · Quantitative Ability · Question 34

Step 1 — write the proportionality.

C=k{w}^{2}

Step 2 — find k from the given piece.

3600=k{\left( 10 \right)}^{2}=100k \Rightarrow k=36

Step 3 — apply it at 4 grams.

C=36\times{4}^{2}=36\times 16=576

Answer: Option 3 — INR 576

Shortcut. Use the ratio directly and skip the constant. Because cost scales with the square of weight,

\frac{{C}_{2}}{{C}_{1}}={\left( \frac{{w}_{2}}{{w}_{1}}\right)}^{2}={\left( \frac{4}{10}\right)}^{2}=\frac{16}{100}

{C}_{2}=3600\times \frac{16}{100}=36\times 16=576

Option (d) INR 1440 is the trap — it is what you get from a linear scaling, 3600\times 4/10. Whenever a quantity varies as a square, the ratio must be squared too; checking that the answer falls much faster than the weight is a quick sanity test.