A total amount of Rs. 7,800 is to be divided between A, B and C in the ratio 1/2 : 1/3 : 1/4. What is the share of B (in Rs.)?

Introduction / Context:
This question involves dividing a given sum of money in a ratio where the ratio terms themselves are fractions. Such questions are slightly more advanced than simple whole number ratios, but they can be solved comfortably by converting the fractional ratio into an equivalent whole number ratio. This technique appears often in aptitude tests involving distribution of money or resources among different people.

Given Data / Assumptions:

Total amount to be divided = Rs. 7,800.
Ratio of shares of A, B and C = 1/2 : 1/3 : 1/4.
All three people together receive the full Rs. 7,800, with no money left over.
We are asked to find the share of B only.

Concept / Approach:
When ratio terms are fractions, a common and efficient method is to clear denominators by multiplying every term by the least common multiple of the denominators. This converts the fractional ratio into an equivalent integer ratio. Then we treat those integers as parts of the total. Each person receives (individual parts / sum of all parts) times the total amount. This keeps the relative proportions exactly the same while making calculations easier.

Step-by-Step Solution:
Original ratio = 1/2 : 1/3 : 1/4. The denominators are 2, 3 and 4. Their least common multiple is 12. Multiply each term in the ratio by 12. A's part becomes (1/2) * 12 = 6, B's part becomes (1/3) * 12 = 4, C's part becomes (1/4) * 12 = 3. So the equivalent integer ratio is 6 : 4 : 3. Total number of parts = 6 + 4 + 3 = 13 parts. Value of one part = 7,800 / 13 = 600. Share of B = 4 parts = 4 * 600 = 2,400 rupees.

Verification / Alternative check:
We can also compute the shares of A and C for a quick consistency check. A gets 6 * 600 = 3,600 and C gets 3 * 600 = 1,800. Then total amount distributed is 3,600 + 2,400 + 1,800 = 7,800, which matches the given total. This confirms that the integer ratio and part calculation are correct.

Why Other Options Are Wrong:
Option 3,600 represents the share of A, who has 6 parts, not B who has 4 parts.
Option 1,800 corresponds to the share of C with 3 parts, so it does not answer the question about B.
Option 1,200 would be equal to 2 parts of 600 each, which does not match the 4 parts required for B according to the derived ratio.

Common Pitfalls:
Some learners forget to convert the fractional ratio into whole numbers and try to work directly with fractions, which can lead to arithmetic mistakes.
Others add the numerators and denominators incorrectly when combining fractions, which distorts the intended ratio.
A common conceptual error is to treat 1/2 : 1/3 : 1/4 as 1:2:3 or some other simplified form, which changes the proportional relationships completely.

Final Answer:
The share of B from the total amount is Rs. 2,400.