Rs 3200 is divided among A, B and C in the ratio 3 : 5 : 8 respectively. What is the difference in rupees between the shares of B and C?

Introduction / Context:
This is a basic ratio and proportion question often seen in aptitude exams. A fixed sum of money is divided among three people in a given ratio, and we are asked to find the difference between the shares of two of them. Such problems strengthen understanding of how to convert ratio parts into actual amounts and how to handle simple comparisons between those amounts.

Given Data / Assumptions:
Total amount to be divided is Rs 3200. The ratio of the shares of A, B and C is 3 : 5 : 8. We need the difference between the shares of B and C. All three receive only this amount and there are no other adjustments or conditions.

Concept / Approach:
When a sum is divided in a ratio, the ratio numbers represent proportional parts of the total. The standard method is to sum the ratio parts, divide the total amount by this sum to find the value of one part, and then multiply by the respective ratio numbers to find individual shares. Finally we find the difference between the specific shares required, which in this question are B and C amounts.

Step-by-Step Solution:
Step 1: Ratio of A : B : C is 3 : 5 : 8. Step 2: Sum of ratio parts = 3 + 5 + 8 = 16. Step 3: Value of one part = total amount / total parts = 3200 / 16. Step 4: Compute 3200 / 16 = Rs 200 per part. Step 5: Share of A = 3 * 200 = Rs 600. Step 6: Share of B = 5 * 200 = Rs 1000. Step 7: Share of C = 8 * 200 = Rs 1600. Step 8: Difference between shares of B and C = 1600 - 1000 = Rs 600.

Verification / Alternative check:
We can verify that the shares add up to the total amount. A share is 600, B share is 1000 and C share is 1600. Their sum is 600 + 1000 + 1600 = 3200, which equals the original total. Additionally, the ratio 600 : 1000 : 1600 simplifies by dividing each term by 200 to 3 : 5 : 8, which matches the given ratio. This confirms that the calculations are consistent and that the difference of Rs 600 is correct.

Why Other Options Are Wrong:
Rs 400 would correspond to a smaller difference and would contradict the derived amounts 1000 and 1600. Rs 800 would suggest that C has 800 more than B, which does not align with the ratio 3 : 5 : 8 when converted to actual values for a total of Rs 3200. Rs 900 is not consistent with any valid combination of shares under the given ratio. Only Rs 600 fits the correct calculation for the difference between Rs 1000 and Rs 1600.

Common Pitfalls:
Some learners divide the total by just one partner ratio number or confuse which shares to subtract. Others may incorrectly treat 3, 5 and 8 as percentages. Always remember to first sum the ratio numbers and then distribute the total proportionally. Clearly writing out each share before subtracting helps avoid sign errors and misinterpretation of the ratio.

Final Answer:
The difference between the shares of B and C is Rs 600.