Q.63
5 skilled workers can build a wall in 20 days;
8 semi-skilled workers can build a wall in 25 days;
10 unskilled workers can build a wall in 30 days.
If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers,
how long will it take to build the wall?
Options:
(A) 20 days
(B) 18 days
(C) 16 days
(D) 15 days
Time and Work Problem: Skilled, Semi-Skilled and Unskilled Workers
Time and work questions are commonly asked in competitive examinations such as
SSC, Banking, Railway, and CAT. These problems are based on converting work
into per-day efficiency and combining different work rates logically.
Question Overview
- 5 skilled workers can build a wall in 20 days
- 8 semi-skilled workers can build a wall in 25 days
- 10 unskilled workers can build a wall in 30 days
If a team consists of 2 skilled, 6 semi-skilled, and 5 unskilled workers,
how long will it take to build the wall?
Concept Used
Work Rate Method:
Work per day = 1 / Time taken
Step-by-Step Solution
Step 1: Individual Worker Efficiency
Skilled workers:
5 skilled workers complete the work in 20 days
1 skilled worker’s rate = 1 / (5 × 20) = 1 / 100
Semi-skilled workers:
8 semi-skilled workers complete the work in 25 days
1 semi-skilled worker’s rate = 1 / (8 × 25) = 1 / 200
Unskilled workers:
10 unskilled workers complete the work in 30 days
1 unskilled worker’s rate = 1 / (10 × 30) = 1 / 300
Step 2: Combined Daily Work Rate
2 skilled workers = 2 × (1 / 100) = 2 / 100
6 semi-skilled workers = 6 × (1 / 200) = 3 / 100
5 unskilled workers = 5 × (1 / 300) = 1 / 60
Total work per day = 2/100 + 3/100 + 1/60
LCM = 300
= (6 + 9 + 5) / 300 = 20 / 300 = 1 / 15
Step 3: Time Required
Time = 1 / (Total work per day)
Time = 15 days
Correct Answer
Option (D): 15 days
Conclusion
By converting each type of worker into daily efficiency and combining their work rates,
the wall will be completed in:
15 days
