Share based on a conditional relation: ₹ 1050 is to be divided among P, Q, and R such that P’s share equals 2/5 of the combined share of Q and R. Find P’s amount received.

Introduction / Context: Distribution problems often provide a relationship between one person’s share and the combined shares of others. Translating this relationship into an equation with the total allows solving for the individual amounts cleanly.

Given Data / Assumptions:

• Total amount = ₹ 1050.
• P = (2/5) * (Q + R).

Concept / Approach: Let S = Q + R. Then P = (2/5)S and total is P + S = 1050. Solve for S, then compute P. This method avoids dealing with Q and R separately.

Step-by-Step Solution:

Verification / Alternative check: Then Q + R = 750, P = 300; total 300 + 750 = 1050—consistent with the given total.

Why Other Options Are Wrong: ₹ 200, ₹ 320, ₹ 420, and ₹ 350 do not satisfy the key relation P = (2/5)(1050 − P).

Common Pitfalls: Misreading the condition as P = 2/5 of the total or as 2/5 of each of Q and R separately; the phrase “combined share of Q and R” means Q + R together.

Final Answer: Rs. 300