A, B, and C can complete a job alone in 20, 25, and 30 days respectively. If they jointly earn Rs. 2,220 for the whole job, by how much does A’s share exceed B’s share?

Introduction / Context: When wages are shared for a job completed together, each person’s share is proportional to their work rate (i.e., 1/time taken alone). We compute shares and then find the difference between A and B.

Given Data / Assumptions:

• A alone: 20 days; B alone: 25 days; C alone: 30 days.
• Total payment = Rs. 2,220 for the whole job.
• Work shares proportional to rates 1/20, 1/25, 1/30.

Concept / Approach: Convert to a common base (e.g., LCM 300). Effective daily works: A = 15, B = 12, C = 10 units. Then divide money in the ratio 15 : 12 : 10 and compare A and B.

Step-by-Step Solution: Work rate ratio = 1/20 : 1/25 : 1/30 = 15 : 12 : 10. Sum parts = 37. A’s share = (15/37) * 2,220; B’s share = (12/37) * 2,220. Difference = (3/37) * 2,220 = 180 (since 2,220/37 = 60).

Verification / Alternative check: Individual shares: A = 900, B = 720, C = 600; they add to 2,220, and A − B = 180.

Why Other Options Are Wrong: Rs. 120, Rs. 300, and Rs. 600 do not match the exact difference from the computed shares.

Common Pitfalls: Dividing by times instead of using rates or missing simplification using the LCM for clean integers.

Final Answer: Rs. 180