Rs. 6300 is divided among A, B and C in the ratio 1/2 : 1 : 3/5. What is the share of B in rupees?

Introduction / Context:
This question deals with the division of a total amount of money among three people in a ratio that involves fractions. Such ratio problems are widely asked in aptitude exams to test a candidate's understanding of fractional ratios and basic arithmetic with proportions. The key is to convert fractional ratios into simple integer ratios and then allocate the total amount according to these parts.

Given Data / Assumptions:

• Total amount = Rs. 6300.
• Ratio of shares of A, B and C is 1/2 : 1 : 3/5.
• We need to find the share of B.
• All amounts are non negative and the entire sum is distributed.

Concept / Approach:
When a total amount is divided in a given ratio, each share is equal to (individual ratio term / sum of ratio terms) * total amount. Here, the ratio terms are fractions: 1/2, 1 and 3/5. It is easier to convert them to equivalent integers. We do this by multiplying all terms by the least common multiple of the denominators. Once the equivalent integer ratio is obtained, we can compute B's share using the standard formula.

Step-by-Step Solution:
Given ratio: A : B : C = 1/2 : 1 : 3/5.Find a common denominator for 2 and 5, which is 10.Multiply each term by 10: (1/2) * 10 = 5, 1 * 10 = 10, (3/5) * 10 = 6.So the simplified integer ratio is A : B : C = 5 : 10 : 6.Total parts = 5 + 10 + 6 = 21.Each part is worth 6300 / 21 rupees.6300 / 21 = 300, so each part is Rs. 300.B has 10 parts, so B's share = 10 * 300 = Rs. 3000.

Verification / Alternative check:
Check A's share: 5 parts * 300 = Rs. 1500.Check B's share: 10 parts * 300 = Rs. 3000.Check C's share: 6 parts * 300 = Rs. 1800.Total = 1500 + 3000 + 1800 = Rs. 6300, which matches the original amount, so the division is correct.

Why Other Options Are Wrong:
Rs. 3300, 2700, 2400 and 2100 do not satisfy the fractional ratio when the corresponding shares of A and C are computed. For example, if B received Rs. 2700, the equivalent part value would be 2700 / 10 = 270, which would give A = 5 * 270 = 1350 and C = 6 * 270 = 1620. The total would then be 1350 + 2700 + 1620 = 5670, not 6300. Hence these alternatives are incorrect.

Common Pitfalls:
The main errors occur when candidates forget to convert fractional ratios to integers or mishandle the denominators. Some students also mistakenly divide 6300 by 3 instead of by the sum of ratio parts. Always remember that the sum used in the denominator is the sum of all ratio terms after simplification, not the number of persons.

Final Answer:
The share of B is Rs. 3000.