Two sums are divided as follows: • First sum: shared among P, Q, and R in the ratio 5 : 6 : 7. • Second sum: shared equally between S and T. If S receives ₹ 2100 less than P, determine how much Q receives from the first sum.

Introduction / Context:
The question mixes two different distributions: one among P, Q, R in a given ratio and another between S and T equally. It links them by stating S gets ₹ 2100 less than P. We must decide whether this information is enough to compute how much Q receives.

Given Data / Assumptions:

• P : Q : R = 5 : 6 : 7 in the first sum (unknown total).
• S = T in the second sum (unknown total).
• S = P − ₹ 2100 (difference only).
• No relation between the two totals is provided.

Concept / Approach:
Amounts in proportional division require the total sum. A single difference constraint between P and S cannot determine the absolute total for the first sum unless a second independent equation links the totals.

Step-by-Step Analysis:
Let first total be X. Then P = 5X/18, Q = 6X/18 = X/3, R = 7X/18. Let second total be Y. Then S = Y/2 and T = Y/2. Given: S = P − 2100 ⇒ Y/2 = 5X/18 − 2100. Unknowns X and Y appear in a single equation; this underdetermines the system. Q = X/3 depends on X, which cannot be uniquely found without another independent condition.

Verification / Alternative check:
Choose example pairs (X, Y) satisfying Y/2 = 5X/18 − 2100; Q = X/3 will vary with X. Hence Q is not uniquely determined.

Why Other Options Are Wrong:
Specific rupee amounts imply a unique X, which we cannot establish from the data. Therefore, any numeric choice is unjustified.

Common Pitfalls:
Assuming the two totals are equal or that one is derived from the other. The question never states such a link, so we must not impose it.

Final Answer:
Couldn't be determined