A man and a boy completed a piece of work in 10 days and were paid ₹10,000.…
2024
A man and a boy completed a piece of work in 10 days and were paid ₹10,000. The man was 50% more efficient than the boy. What is the difference between their daily wages?
Answer: D. ₹200 — ConceptWhen workers are paid in proportion to their contribution, their wage ratio equals their efficiency ratio if they work for the same duration. If the…
- A.
₹100
- B.
₹500
- C.
₹400
- D.
₹200
Attempted by 2 students.
Show answer & explanation
Correct answer: D
Concept
When workers are paid in proportion to their contribution, their wage ratio equals their efficiency ratio if they work for the same duration.
If the efficiency ratio is a:b and the combined payment per day is T, their daily wages are aT/(a+b) and bT/(a+b).
Application
Let the boy’s efficiency be 2 units. Being 50% more efficient, the man’s efficiency is 2 × 1.5 = 3 units, so the efficiency ratio is 3:2.
The combined payment per day is ₹10,000 ÷ 10 = ₹1,000.
The man’s daily wage is ₹1,000 × 3/5 = ₹600.
The boy’s daily wage is ₹1,000 × 2/5 = ₹400.
Their daily-wage difference is ₹600 − ₹400 = ₹200.
Cross-check
The daily wages ₹600 and ₹400 add to ₹1,000, and their ratio 600:400 simplifies to 3:2, matching the efficiency ratio.
Result
The difference between the daily wages is ₹200.