Rs. 6,300 is divided among A, B and C in the ratio 1/2 : 1 : 3/5. If these fractional terms represent their proportional shares, what is the share of B in rupees?

Introduction / Context:
This problem deals with distributing a fixed sum according to a ratio that is given in fractional form. Instead of simple integers, the shares of A, B and C are in the ratio 1/2 : 1 : 3/5. We must convert these fractions into a simple integer ratio and then use it to find B's share from the total amount of Rs. 6,300.

Given Data / Assumptions:

• Total amount to be divided is Rs. 6,300.
• Ratio of shares of A : B : C is 1/2 : 1 : 3/5.
• We need to find the share of B.

Concept / Approach:
When a ratio is given in fractions, the first step is to convert them to a common denominator and express the ratio as whole numbers. Then the usual method of ratio distribution is applied: we sum the ratio parts, find how much money each part represents and multiply by the number of parts corresponding to B. This process ensures that the fractions are correctly handled.

Step-by-Step Solution:
Step 1: The given ratio is A : B : C = 1/2 : 1 : 3/5.Step 2: Convert all fractions to a common denominator, which is 10.Step 3: 1/2 = 5/10, 1 = 10/10, and 3/5 = 6/10.Step 4: The ratio in terms of numerators is A : B : C = 5 : 10 : 6.Step 5: Sum of the ratio parts = 5 + 10 + 6 = 21.Step 6: Each ratio part corresponds to 6,300 / 21 = 300 rupees.Step 7: B has 10 parts, so B's share = 10 * 300 = Rs. 3,000.

Verification / Alternative check:
We can verify by computing all shares. A's share = 5 * 300 = Rs. 1,500. B's share = 3,000. C's share = 6 * 300 = Rs. 1,800. Adding them up gives 1,500 + 3,000 + 1,800 = Rs. 6,300, which matches the total. The ratio 1,500 : 3,000 : 1,800 simplifies to 1/2 : 1 : 3/5 when expressed back as fractions relative to a common value, confirming the correctness of the distribution.

Why Other Options Are Wrong:
If B's share were 3,300, the remaining 3,000 would not fit the 5 : 10 : 6 ratio. Values like 2,700 and 4,200 also lead to inconsistent ratios when the remaining amounts are checked. 'None of these' is incorrect because Rs. 3,000 matches the required ratio and total sum perfectly.

Common Pitfalls:
Some learners directly interpret 1/2 : 1 : 3/5 as 1 : 2 : 3 without adjusting for the denominators, which is wrong. Others forget to divide the total by the sum of ratio parts and instead multiply incorrectly. Always convert fraction ratios to whole number ratios using a common denominator, then apply the standard ratio distribution method.

Final Answer:
The share of B from the total amount is Rs. 3,000.