A certain amount of money is divided among three partners P, Q and R in the ratio 3 : 7 : 6 respectively. If the difference between the share of P and the share of Q is Rs. 2700, what is the share of R in the total amount?

Introduction / Context:
This aptitude question is based on the concept of dividing an amount of money in a given ratio and then using the difference between two shares to find the unknown share of a third person. Such questions are common in competitive exams under the topic of partnership and ratio proportion.

Given Data / Assumptions:

• The amount is divided among P, Q and R in the ratio 3 : 7 : 6.
• The difference between the share of P and the share of Q is Rs. 2700.
• We need to find the share of R.
• The total amount is not directly required for the calculation.

Concept / Approach:
When an amount is divided in a ratio, each share is equal to ratio part multiplied by a common multiplying factor. The difference between any two shares is equal to the difference in their ratio parts multiplied by this same factor. By using the given difference, we can first find the factor and then use it to calculate the required share of R.

Step-by-Step Solution:
Step 1: Let the common multiplying factor be k. Then the shares are: P = 3k, Q = 7k, R = 6k. Step 2: The difference between the share of Q and the share of P is given as Rs. 2700. So, 7k - 3k = 4k. Step 3: Set this equal to the given difference: 4k = 2700. Step 4: Find k by dividing 2700 by 4. k = 2700 / 4 = 675. Step 5: Now calculate the share of R which is 6k. R = 6 * 675 = 4050. Step 6: Therefore the share of R in the total amount is Rs. 4050.

Verification / Alternative check:
We can quickly verify the logic by calculating the actual shares of P and Q. P gets 3 * 675 = Rs. 2025. Q gets 7 * 675 = Rs. 4725. The difference between these two amounts is 4725 - 2025 = Rs. 2700, which matches the given difference. Since R is 6 * 675 = Rs. 4050, our calculation is consistent with the ratio and the condition in the question, so the answer is reliable.

Why Other Options Are Wrong:
Rs. 2121 is not a multiple of 675, so it cannot match the ratio 3 : 7 : 6.
Rs. 5040 would correspond to a factor of 840 which does not satisfy the difference condition of Rs. 2700 between P and Q.
Rs. 3550 is neither a multiple of 675 nor consistent with the given ratio, so it cannot be correct.

Common Pitfalls:
One common mistake is to assume that the difference of 2700 is between the shares of Q and R rather than between P and Q. Another error is to try to find the total amount first, which is unnecessary and can waste time. Some learners also forget that the same common factor k must be used for all three shares once the ratio is given. Working directly with the ratio difference is simpler and less error prone.

Final Answer:
The share of R in the total amount is Rs. 4050.