Proportional division with linked ratios: A total of ₹ 7000 is divided among A, B, and C. The shares of A and B are in the ratio 2 : 3, and the shares of B and C are in the ratio 4 : 5. Find the exact amount received by B.

Introduction / Context:
This problem tests chained-ratio division of a fixed sum of money. We are given two compatible ratios that share a common term (B), and we must use them together to determine each person’s share, especially B’s amount.

Given Data / Assumptions:

• Total amount = ₹ 7000.
• A : B = 2 : 3.
• B : C = 4 : 5.
• All shares are positive and add up to the total.

Concept / Approach:
Let A = 2x and B = 3x from the first ratio. Also let B = 4y and C = 5y from the second ratio. Since B is common, equate 3x = 4y to connect the two parameterizations. Use the total sum to solve for x (or y), then compute B.

Step-by-Step Solution:
From 3x = 4y ⇒ y = 3x/4.A + B + C = 2x + 3x + 5y = 5x + 5y.Substitute y: total = 5x + 5*(3x/4) = 5x + 15x/4 = 35x/4.35x/4 = 7000 ⇒ x = 800.B = 3x = 2400.

Verification / Alternative check:
Compute all shares: A = 1600, B = 2400, C = 3000 (since y = 600 and C = 5y = 3000). The ratios 2 : 3 and 4 : 5 are satisfied and the sum is 7000.

Why Other Options Are Wrong:

• ₹ 1600 and ₹ 2000 are smaller than B’s required 3-part share.
• ₹ 3000 corresponds to C’s share when constraints are satisfied.

Common Pitfalls:

• Treating the two ratios independently without equating the common term B.
• Forgetting to use the total to fix the scale of the ratios.

Final Answer:
₹ 2400