Work and Wages – B’s share when A and B finish together: Individually A needs 30 days and B needs 40 days to complete a job. They finish together and receive $2100. What is B’s share?

Introduction / Context:
For constant-rate workers, wage shares are proportional to their work rates. Since both worked for the same time together, use rates directly to split the total payment.

Given Data / Assumptions:

• A’s time = 30 days ⇒ rate = 1/30
• B’s time = 40 days ⇒ rate = 1/40
• Total payment = $2100

Concept / Approach:
Ratio A:B = (1/30):(1/40) = 40:30 = 4:3. Thus B’s share is 3/7 of the total.

Step-by-Step Solution:
Total ratio parts = 4 + 3 = 7B’s share = 3/7 * 2100 = $900

Verification / Alternative check:
A’s share = 4/7 * 2100 = $1200; together $2100.

Why Other Options Are Wrong:
$1200 is A’s share; $800, $1300, and $750 do not equal 3/7 of $2100.

Common Pitfalls:
Using time ratio 30:40 directly; always use rate ratio (reciprocals).

Final Answer:
$900