Equalized expressions from three shares: ₹ 600 is divided among A, B, and C such that the following three values are equal: 40 more than 2/5 of A’s share, 20 more than 2/7 of B’s share, and 10 more than 9/17 of C’s share. Find B’s share.

Introduction / Context:
This algebraic division question equates three different linear expressions of A, B, and C to a common value. Expressing each share in terms of that common value, and then using the total, allows us to solve the system easily.

Given Data / Assumptions:

• Total = ₹ 600.
• 2/5 A + 40 = 2/7 B + 20 = 9/17 C + 10 = k (say).

Concept / Approach:
From the equalities, write A, B, and C in terms of k: A = (5/2)(k − 40), B = (7/2)(k − 20), C = (17/9)(k − 10). Sum them to 600 to solve for k, then find B explicitly.

Step-by-Step Solution:
A = 5/2 (k − 40) = 2.5k − 100.B = 7/2 (k − 20) = 3.5k − 70.C = 17/9 (k − 10) = (17/9)k − 170/9.Sum: (5/2 + 7/2 + 17/9)k − (100 + 70 + 170/9) = 600.(71/9)k − 1700/9 = 600 ⇒ 71k − 1700 = 5400 ⇒ 71k = 7100 ⇒ k = 100.B = 7/2 (100 − 20) = 7/2 * 80 = ₹ 280.

Verification / Alternative check:
Compute A and C: A = 5/2 * 60 = 150; C = 17/9 * 90 ≈ 170; total 150 + 280 + 170 = 600. All three expressions equal k = 100, by construction.

Why Other Options Are Wrong:

• ₹ 150 and ₹ 170 (not listed) align with A or C, not B.
• ₹ 185 and ₹ 285 come from arithmetic slips in solving for k or substituting into B.

Common Pitfalls:

• Mistakes in fractional arithmetic when summing coefficients.
• Forgetting that each expression equals the same k.

Final Answer:
₹ 280