Divide Rs. 600 among A, B, and C so that Rs. 40 more than 2/5 of A’s share, Rs. 20 more than 2/7 of B’s share, and Rs. 10 more than 9/17 of C’s share are all equal. What is A’s share?

Introduction / Context:
This distribution problem sets three expressions (each a fraction of a share plus a constant) to be equal. We introduce a common value, express each share in terms of it, and satisfy the total sum constraint to find each person’s share—specifically A’s.

Given Data / Assumptions:

• Let the common equal value be k.
• 2/5 of A + 40 = k ⇒ A = (5/2)(k − 40).
• 2/7 of B + 20 = k ⇒ B = (7/2)(k − 20).
• 9/17 of C + 10 = k ⇒ C = (17/9)(k − 10).
• A + B + C = 600.

Concept / Approach:
Express all three shares in terms of k, then add and set equal to 600. Solve for k, then compute A’s share directly using A = (5/2)(k − 40).

Step-by-Step Solution:
A = (5/2)(k − 40). B = (7/2)(k − 20). C = (17/9)(k − 10). Sum: (5/2)(k − 40) + (7/2)(k − 20) + (17/9)(k − 10) = 600. Solving gives k = 100. A = (5/2)(100 − 40) = (5/2)*60 = 150.

Verification / Alternative check:
Compute B = (7/2)*80 = 280; C = (17/9)*90 = 170; total 150 + 280 + 170 = 600. Also, checks: 2/5 of 150 + 40 = 60 + 40 = 100; 2/7 of 280 + 20 = 80 + 20 = 100; 9/17 of 170 + 10 = 90 + 10 = 100—consistent.

Why Other Options Are Wrong:
Rs. 280 and Rs. 170 correspond to B and C shares, not A. Rs. 200 does not satisfy all three equality conditions.

Common Pitfalls:
Forgetting to set all three expressions equal to a single k, or mishandling fractional coefficients. Work symbolically and then verify by back-substitution.

Final Answer:
Rs. 150