A quarter kilogram of carrots costs 60 paise. At the same rate, how many paise will 200 grams of carrots cost?

Introduction / Context:
This question is a simple unitary method or chain rule problem involving proportional cost with respect to weight. The idea is that if you know the cost of a certain quantity, you can find the cost of any other quantity of the same item at the same rate. Such problems are very common in shopping, billing, and basic arithmetic aptitude.

Given Data / Assumptions:

• Cost of 1/4 kilogram of carrots (that is, 250 grams) is 60 paise.
• The price per gram is constant.
• We need to find the cost of 200 grams of carrots.

Concept / Approach:
Since cost is directly proportional to weight, we can either find the cost per gram and multiply by 200, or use a simple ratio between 250 grams and 200 grams. The unitary method says that if cost for some quantity is known, cost for 1 unit is total cost divided by quantity, and then we multiply by required quantity.

Step-by-Step Solution:
Step 1: A quarter kilogram is 250 grams.Step 2: Cost for 250 grams = 60 paise.Step 3: Cost per gram = 60 / 250 paise.Step 4: Required cost for 200 grams = (60 / 250) * 200.Step 5: Compute: 60 * 200 / 250 = 60 * (4 / 5) = 48 paise.

Verification / Alternative check:
We can also use a direct ratio. If 250 grams cost 60 paise, then 200 grams is 200 / 250 of this weight, which is 4 / 5 of 250 grams. Therefore cost for 200 grams is 4 / 5 of 60 paise, which is again 48 paise. Both approaches confirm the same value.

Why Other Options Are Wrong:
40 and 42 paise are below the correct proportional value and would correspond to a lower rate than stated. 52 paise is slightly above the correct value and would give a higher price per gram. 60 paise is the cost for 250 grams, not for 200 grams, so it cannot be correct for the smaller quantity.

Common Pitfalls:

• Using 200 / 250 incorrectly as 5 / 4 instead of 4 / 5.
• Forgetting to convert quarter kilogram into grams and directly comparing 1/4 and 200 without a common unit.
• Rounding too early instead of keeping exact fractions until the last step.

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