A, B, and C share a sum in the ratio 2 : 3 : 7. If A and B together receive Rs. 1,500 less than C, what is A’s share?

Introduction / Context:
This is a ratio allocation with an extra condition comparing a combined share to another. We set the common multiplier and solve using the given difference to find A’s share.

Given Data / Assumptions:

• A : B : C = 2 : 3 : 7.
• (A + B) is Rs. 1,500 less than C.
• Find A’s amount.

Concept / Approach:
Let shares be 2k, 3k, 7k. Then (2k + 3k) = 7k − 1,500 ⇒ 5k = 7k − 1,500. Solve for k and then compute A = 2k.

Step-by-Step Solution:
5k = 7k − 1,500 ⇒ 2k = 1,500 ⇒ k = 750. A’s share = 2k = 1,500.

Verification / Alternative check:
B = 3k = 2,250; C = 7k = 5,250. Then A + B = 3,750 which is Rs. 1,500 less than 5,250, matching the condition.

Why Other Options Are Wrong:
Rs. 1,000 and Rs. 2,000 do not satisfy the difference condition when ratios are respected. “Date inadequate” is incorrect; data is sufficient.

Common Pitfalls:
Misinterpreting “less than” or mixing the roles of A + B and C. Always express all in a single variable k first.

Final Answer:
Rs. 1500