Rs. 1300 is divided among A, B, C, and D such that A/B = B/C = C/D = 2/3 (i.e., in continued proportion). What is A’s share?

Introduction / Context:
The shares are in continued proportion with common ratio 3/2 from each to the next. We use a geometric progression approach to express all shares in terms of A and then match the total to Rs. 1300.

Given Data / Assumptions:

• A/B = B/C = C/D = 2/3.
• Total sum = Rs. 1300.
• Find A’s share.

Concept / Approach:
From A/B = 2/3, we get B = (3/2)A; then C = (3/2)B = (3/2)^2 A; D = (3/2)^3 A. Sum these four terms and equate to 1300 to solve for A.

Step-by-Step Solution:
S = A + (3/2)A + (3/2)^2 A + (3/2)^3 A. Compute factors: 1 + 1.5 + 2.25 + 3.375 = 8.125. Thus, 8.125A = 1300 ⇒ A = 1300 / 8.125. 8.125 = 65/8 ⇒ A = 1300 * 8 / 65 = 160. Hence A’s share = Rs. 160.

Verification / Alternative check:
Compute other shares and sum to 1300; the arithmetic will check out with A = 160.

Why Other Options Are Wrong:
Rs. 140, Rs. 240, Rs. 320 do not satisfy the continued-proportion sum equaling 1300.

Common Pitfalls:
Treating the ratio as simple proportion instead of continued proportion or summing only two or three terms. All four must be included.

Final Answer:
Rs. 160