Rs. 2018 is to be divided among P, Q and R such that whenever P gets Rs. 5, Q must get Rs. 12, and whenever Q gets Rs. 4, R must get Rs. 5.50. By how much (in rupees) does the share of R exceed the share of Q?

Introduction / Context:
This question deals with proportional division of a sum among three people P, Q and R based on pairwise conditions. Such problems often appear in the partnership or ratio and proportion section of aptitude tests. The goal is not to find each individual share directly at first but to determine the ratio of their shares using the given conditional statements and then use the total amount to compute the required difference between two shares.

Given Data / Assumptions:

• Total amount to be divided among P, Q and R is Rs. 2018.
• If P receives Rs. 5, then Q must receive Rs. 12.
• If Q receives Rs. 4, then R must receive Rs. 5.50.
• The above conditions describe proportional relationships that hold for their entire shares.
• We need the amount by which R's share exceeds Q's share.

Concept / Approach:
The conditions describe ratios between pairs of shares. The statement that if P gets Rs. 5, Q gets Rs. 12 implies that P : Q = 5 : 12. Similarly, if Q gets Rs. 4 and R gets Rs. 5.50, then Q : R = 4 : 5.5, which can be converted into a simpler integer ratio. Once we have P : Q and Q : R, we combine them to obtain P : Q : R. Then we express the total amount as a sum of these ratio parts, find the value per part, and finally compute R minus Q.

Step-by-Step Solution:
Step 1: From the first condition, P : Q = 5 : 12. Step 2: From the second condition, Q : R = 4 : 5.5. Multiply both terms by 2 to remove the decimal and obtain Q : R = 8 : 11. Step 3: Now express P, Q and R in a common ratio form. From P : Q = 5 : 12, write P : Q = 5 : 12. From Q : R = 8 : 11, write Q : R = 8 : 11. Step 4: Make the value of Q the same in both ratios. The least common multiple of 12 and 8 is 24. Step 5: Multiply P : Q = 5 : 12 by 2 to get P : Q = 10 : 24. Step 6: Multiply Q : R = 8 : 11 by 3 to get Q : R = 24 : 33. Step 7: Combine to obtain P : Q : R = 10 : 24 : 33. Step 8: Total ratio parts are 10 + 24 + 33 = 67. So each part is approximately 2018 / 67. Step 9: The difference between R and Q in parts is 33 minus 24 = 9 parts. So the required difference is 9 * (2018 / 67). Step 10: Compute 2018 / 67 = 30.1194 (approximately), and 9 * 30.1194 is about 271. So the difference is Rs. 271 (to the nearest rupee).

Verification / Alternative check:
To verify, take each part as approximately Rs. 30.12 and compute the three shares. P gets 10 * 30.12 ≈ 301.2, Q gets 24 * 30.12 ≈ 722.88 and R gets 33 * 30.12 ≈ 994.0. Adding these gives approximately 2018, matching the total. The difference R minus Q is close to 994.0 minus 722.9 which is around Rs. 271. This confirms that Rs. 271 is the most reasonable integer value for the required difference given the slight rounding due to the original sum.

Why Other Options Are Wrong:
The other options such as Rs. 127, Rs. 217, Rs. 251 and Rs. 721 do not agree with the ratio P : Q : R = 10 : 24 : 33 when checked against the total of Rs. 2018. Using any of these values as the difference between R and Q would disturb the ratio and fail to sum correctly to the total amount. Only Rs. 271 fits the ratio and the total sum at the same time.

Common Pitfalls:
Learners often forget to convert ratios involving decimals into whole numbers or fail to align the middle term (Q) correctly when combining two ratios. Some also attempt to compute individual shares first without establishing the ratio, which usually leads to mistakes. Another common error is to round off intermediate results too early, which can create small discrepancies. Always convert to integer ratios, combine carefully and delay rounding until the final answer is needed.

Final Answer:
The share of R exceeds the share of Q by approximately Rs. 271, which matches option B.