Work and Wages – Wage split by efficiency (rates add when working together): Shantanu completes a job in 12 days; Manu completes the same job in 10 days. If they work together and are paid proportionally to work done, in what ratio should their wages be divided?

Introduction / Context:
When workers are paid according to contribution, their wage shares are proportional to the amount of work each performs. For constant-rate workers, that equals their rates (work per day). Combining workers adds rates, but the internal split uses their individual rates.

Given Data / Assumptions:

• Shantanu’s time = 12 days ⇒ rate = 1/12 job/day
• Manu’s time = 10 days ⇒ rate = 1/10 job/day
• Payment split is proportional to rates.

Concept / Approach:
Wage ratio = (1/12) : (1/10). Multiply through by the LCM to clear denominators and get clean integers for the ratio.

Step-by-Step Solution:
(1/12) : (1/10) = 10 : 12Simplify 10 : 12 to 5 : 6

Verification / Alternative check:
Using a common-work model: in 60 days (LCM), Shantanu would do 5 units, Manu 6 units; hence wages 5:6.

Why Other Options Are Wrong:
3:2, 1:6, and 5:7 do not match the reciprocal-time ratio; 6:5 reverses the correct order.

Common Pitfalls:
Splitting by times taken (12:10) instead of by rates; remember wage ∝ rate, not time.

Final Answer:
5 : 6