Fractional ratio conversion and split: ₹ 1664 is divided between P and Q in the ratio 1/3 : 1/5. Convert this to an integer-part ratio and determine P’s share precisely.

Introduction / Context:
Ratios given as fractions can be scaled to whole-number parts by clearing denominators. Then the standard part-of-whole method yields each person’s share from the total amount.

Given Data / Assumptions:

• P : Q = (1/3) : (1/5).
• Total = ₹ 1664.

Concept / Approach:
Multiply both ratio terms by the least common multiple of denominators (15) to get whole parts: 5 : 3. Then find one-part value and scale for P’s part (5 parts).

Step-by-Step Solution:

Verification / Alternative check:
Q’s share = 3 * 208 = ₹ 624. Sum = 1040 + 624 = 1664, matching the given total and preserving the 5 : 3 split.

Why Other Options Are Wrong:
1085, 1015, 1090, and 980 do not correspond to 5/8 of ₹ 1664.

Common Pitfalls:
Adding numerators/denominators directly or interpreting 1/3 : 1/5 as 1 : 1; remember to clear denominators to get integer parts.

Final Answer:
1040