If a quarter kilogram (250 g) of carrots costs 60 paise, then, at the same rate, how many paise will 200 grams of carrots cost?

Introduction / Context:
This is a simple unitary-method question involving direct proportion between quantity and cost. It checks whether you can scale prices correctly when the weight changes, a very common topic in basic arithmetic and aptitude tests.

Given Data / Assumptions:
- 1 quarter kilogram = 250 grams of carrots costs 60 paise.
- We need the cost of 200 grams of carrots at the same rate per gram.
- The cost is directly proportional to the weight when the rate per gram is constant.

Concept / Approach:
Because price ∝ quantity for a fixed unit rate, we can either compute the cost per gram and multiply by 200, or directly apply a fraction relating 200 g to 250 g. Both methods should lead to the same answer, demonstrating proportional reasoning.

Step-by-Step Solution:
Step 1: Recognise that 250 g of carrots cost 60 paise.Step 2: Cost per gram = total cost / total grams = 60 / 250 paise per gram.Step 3: For 200 g, cost = (60 / 250) * 200 paise.Step 4: Simplify: (60 * 200) / 250 = 12,000 / 250.Step 5: 12,000 / 250 = 48 (since 250 * 48 = 12,000).Step 6: Therefore, 200 g of carrots cost 48 paise.

Verification / Alternative check:
Use simple fraction scaling: 200 g is (200 / 250) = 4 / 5 of 250 g. Therefore, the cost for 200 g is 4 / 5 of 60 paise. Compute 4 / 5 * 60 = 4 * 12 = 48 paise. This confirms the earlier result obtained by the unitary method.

Why Other Options Are Wrong:
54 or 62 paise correspond to using an incorrect fraction or miscomputing the division. 78 paise is more than the cost of 250 g and thus clearly impossible for a smaller quantity like 200 g. 40 paise would correspond to a different per-gram rate and does not match the given 60 paise for 250 g relationship.

Common Pitfalls:
Common mistakes include treating 200 g as 3/4 or 2/3 of 250 g instead of 4/5, or simplifying 12,000 / 250 incorrectly. Another issue is confusing paise and rupees, but here everything is in paise. Carefully setting up the proportional fraction and doing the arithmetic stepwise will avoid these errors.

Final Answer:
The cost of 200 grams of carrots is 48 paise.