Introduction / Context:
This time and work problem focuses on sharing wages in proportion to the work done by each worker. A, B and C complete different portions of the total work, and the total wage amount must be divided fairly among them. You are then asked to find the effective daily wage for each person.
Given Data / Assumptions:
- A can finish the entire work in 10 days.
- B can finish the entire work in 15 days.
- A and B work together for 5 days.
- C completes the remaining work alone in 2 days.
- Total wages for the complete work = Rs 3000.
- Wages are divided in proportion to work done by each person.
Concept / Approach:
We first convert total work into abstract units using a convenient least common multiple of days. Each person then gets a work rate per day. From this, we can compute how many units A, B and C complete. Their wage shares are proportional to these completed units. Finally, divide each person's share by the number of days they worked to find individual daily wages.
Step-by-Step Solution:
Assume total work W has 30 units (LCM of 10 and 15).
A's rate = 30 / 10 = 3 units per day.
B's rate = 30 / 15 = 2 units per day.
Let C's rate be c units per day.
In 5 days, work done by A and B together = 5 * (3 + 2) = 25 units + 5c? Actually C is not working yet, so they do 5 * (3 + 2) = 25 units.
Remaining work = 30 - 25 = 5 units.
C completes 5 units in 2 days, so C's rate c = 5 / 2 = 2.5 units per day.
Now total work by A = 3 * 5 = 15 units.
Total work by B = 2 * 5 = 10 units.
Total work by C = 2.5 * 2 = 5 units.
Work ratio A : B : C = 15 : 10 : 5 = 3 : 2 : 1.
Total wage Rs 3000, so one share = 3000 / 6 = Rs 500.
A's wage = 3 * 500 = Rs 1500.
B's wage = 2 * 500 = Rs 1000.
C's wage = 1 * 500 = Rs 500.
Daily wages: A worked 5 days, so 1500 / 5 = Rs 300 per day.
B worked 5 days, so 1000 / 5 = Rs 200 per day.
C worked 2 days, so 500 / 2 = Rs 250 per day.
Verification / Alternative check:
The sum of daily wages times days = 300 * 5 + 200 * 5 + 250 * 2 = 1500 + 1000 + 500 = Rs 3000, which matches the total wage.
Why Other Options Are Wrong:
200, 250, 300 would not respect the correct work ratio; the highest wage should go to A, not C.
200, 300, 400 and similar patterns give total wages or sharing ratios different from 3 : 2 : 1.
Therefore only 300, 200, 250 matches both proportional work and total amount.
Common Pitfalls:
Some learners mistakenly distribute wages according to time worked alone, ignoring different efficiencies.
Another error is to forget that C works only for 2 days, but A and B work for 5 days, so daily wages are not the same as total wages.
Always base wage distribution on work done (units completed), not merely on days present.
Final Answer:
The daily wages are Rs 300, Rs 200 and Rs 250 for A, B and C respectively.
Discussion & Comments