A can complete a job in 10 days and B in 15 days. They work together for 5 days; the remaining work is finished by C in 2 more days. If the total wage for the job is Rs 3000 and payment is proportional to work done, what are the daily wages of A, B, and C, respectively?
Correct Answer: 300, 200, 250
Introduction / Context:Wages proportional to work implies each person’s pay equals (their completed fraction of the job) times total wages. Daily wage equals that person’s pay divided by the number of days they worked.
Given Data / Assumptions:
- A’s time = 10 days ⇒ rate = 1/10 job/day.
- B’s time = 15 days ⇒ rate = 1/15 job/day.
- C completes the remainder in 2 days after A and B worked together for 5 days.
- Total wage = Rs 3000.
Concept / Approach:Use an LCM work-unit model. Let total job = 30 units. Then A = 3 units/day; B = 2 units/day. In 5 days together they do 25 units, leaving 5 units. C does 5 units in 2 days ⇒ 2.5 units/day. Split pay by units; then divide each person’s pay by their worked days to get daily wages.
Step-by-Step Solution:
A’s contribution = 3 * 5 = 15 units.B’s contribution = 2 * 5 = 10 units.C’s contribution = 5 units (over 2 days).Total = 30 units ⇒ Rs per unit = 3000 / 30 = Rs 100.Pays: A = 1500, B = 1000, C = 500.Daily wages: A = 1500/5 = 300; B = 1000/5 = 200; C = 500/2 = 250.Verification / Alternative check:Daily wages reflect each one’s productivity and time; sums consistent with total Rs 3000.
Why Other Options Are Wrong:Other triples do not honor the proportional split and days worked.
Common Pitfalls:Splitting by time instead of work; forgetting to divide by days to get daily wages.
Final Answer:300, 200, 250