Q.6
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?
Skilled Workers Wall 20 Days Semi-Skilled 25 Days Unskilled 30 Days Team Time
15 days is the correct answer: A team of 2 skilled, 6 semi-skilled, and 5 unskilled workers will take 15 days to build the wall.
Work Rate Calculation
Assume total wall work is 100 units (LCM of denominators for simplicity).
- 5 skilled workers complete 100 units in 20 days → 1 skilled: 1/100 units/day
- 8 semi-skilled complete 100 units in 25 days → 1 semi-skilled: 1/200 units/day
- 10 unskilled complete 100 units in 30 days → 1 unskilled: 1/300 units/day
Team rate: 2 × 1/100 + 6 × 1/200 + 5 × 1/300 = 2/100 + 6/200 + 5/300 = 0.02 + 0.03 + 0.0167 = 0.0667 units/day (1/15). Time: 100 / (100/15) = 15 days.
Option Explanations
| Option | Why Incorrect/Correct |
|---|---|
| 20 days | Matches skilled alone; ignores faster team mix |
| 18 days | Possible miscalculation (e.g., wrong LCM) |
| 10 days | Overestimates rates, like equalizing all skills |
| 15 days | Exact match from rates; correct |
5 Skilled Workers Build Wall in 20 Days – Complete Solution
5 skilled workers build a wall in 20 days, 8 semi-skilled in 25 days, 10 unskilled in 30 days—how long for 2 skilled, 6 semi-skilled, 5 unskilled team? This GATE-style work rate problem highlights combined efficiencies for exam prep.
Step-by-Step Solution
Find individual rates assuming 100-unit wall: Skilled (1/100/day), semi (1/200), unskilled (1/300). Team totals 1/15 work/day, so 15 days.
Common Mistakes
Forgetting to scale rates leads to 20 or 18 days errors. Verify with LCM for accuracy.
