A and B together have a total of ₹6300. If (5/19) of A's money is equal to (2/5) of B's money, find how much money B has in rupees.

Introduction / Context:
This problem is a typical ratio and linear equation question based on money distribution between two people. You are given the total amount of money they share and a relationship between fractions of their individual amounts. The task is to use this information to determine how much money B has. Problems of this type frequently appear in quantitative aptitude sections of competitive exams and require careful handling of fractions and ratios.

Given Data / Assumptions:

• The total money held by A and B together is ₹6300.
• (5/19) of A's amount is equal to (2/5) of B's amount.
• All amounts are in rupees and are non negative.
• We must find the amount of money B has.

Concept / Approach:
Let A's money be A and B's money be B. We are given a fractional relation: (5/19) * A = (2/5) * B. From this equation, we can derive a ratio between A and B. Once we know A : B, we can express both amounts in terms of a common multiplier and then use the total A + B = 6300 to determine that multiplier and finally B. This is a standard method for solving ratio problems involving totals and fractional relationships.

Step-by-Step Solution:
1) Let A's amount be A and B's amount be B. 2) The condition is (5/19) * A = (2/5) * B. 3) Clear fractions by multiplying both sides by 19 * 5: (5/19) * A * 19 * 5 = (2/5) * B * 19 * 5. 4) On the left side, 19 cancels 19 in the denominator and 5 remains, giving 25A. On the right side, 5 cancels 5 and we get 38B. 5) This simplifies to 25A = 38B. 6) Rearranging gives A / B = 38 / 25, so the ratio A : B = 38 : 25. 7) Let A = 38k and B = 25k for some positive constant k. 8) Use the total amount A + B = 6300: 38k + 25k = 63k = 6300. 9) Solve for k: k = 6300 / 63 = 100. 10) Now compute B: B = 25k = 25 * 100 = 2500.

Verification / Alternative check:
Verify that these values satisfy the original conditions. With k = 100, we have A = 38 * 100 = 3800 and B = 2500. First, check the total: A + B = 3800 + 2500 = 6300, which matches the given total. Next, check the fractional relation. Compute (5/19) of A: (5/19) * 3800 = 5 * 200 = 1000. Compute (2/5) of B: (2/5) * 2500 = 2 * 500 = 1000. Both sides are equal, confirming that the relationship holds and that B = ₹2500 is correct.

Why Other Options Are Wrong:
Option b (₹2300), option c (₹3800), option d (₹4000), and option e (₹3000) do not satisfy both the total and the fractional condition simultaneously. For example, if B were ₹3000, then A would be ₹3300, and (5/19) of A would not equal (2/5) of B. Only B = ₹2500 produces consistent values that match the given constraints.

Common Pitfalls:
A common mistake is to handle the fractional equation incorrectly, such as cross multiplying without clearing denominators properly, or misinterpreting (5/19) of A as A * 19 / 5. Another frequent error is to form the ratio A : B incorrectly from 25A = 38B. Keeping the algebraic steps clear and verifying with the total sum at the end helps avoid these mistakes.

Final Answer:
B's share of the money is ₹2500.