Share work payment by efficiency (rates): A, B, and C can complete a job in 20, 25, and 30 days respectively. They finish the work together for Rs. 2220. By how much does A’s share exceed B’s share?

Introduction / Context:
When workers are paid for a completed job, the fair division is proportional to the work each performs. For constant-rate workers, work done is proportional to their rates, which are inversely proportional to their individual times to complete the task alone.

Given Data / Assumptions:

• A = 20 days, B = 25 days, C = 30 days.
• Total payment = Rs. 2220.
• Share ∝ 1/day count.

Concept / Approach:
Compute rate proportions using a convenient LCM of days (e.g., 300). Then divide the total in the ratio of rates, and compare A and B’s shares.

Step-by-Step Solution:
LCM = 300 ⇒ A’s rate = 300/20 = 15, B’s = 300/25 = 12, C’s = 300/30 = 10.Ratio = 15 : 12 : 10; sum = 37.Each “ratio unit” = 2220 / 37 = 60.A’s share = 15 * 60 = 900; B’s share = 12 * 60 = 720.Difference = 900 − 720 = Rs. 180.

Verification / Alternative check:
C’s share = 10 * 60 = 600; total 900 + 720 + 600 = 2220, consistent.

Why Other Options Are Wrong:

• 120 and 300 are arithmetic misreads of the 60-unit scaling.
• 600 is the entire share of C, not the difference A − B.

Common Pitfalls:

• Dividing in the ratio of days (20 : 25 : 30) instead of rates.

Final Answer:
Rs. 180