5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build…
2010
5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?
- A.
20
- B.
18
- C.
16
- D.
15
Attempted by 45 students.
Show answer & explanation
Correct answer: D
Key insight: Find each worker's daily rate, then add the rates for the whole team to get the team's daily work rate.
Compute per-worker daily rates:
A skilled worker: 5 skilled finish in 20 days ⇒ group rate = 1/20, so one skilled worker = 1/(5×20) = 1/100 of the wall per day.
A semi-skilled worker: 8 semi-skilled finish in 25 days ⇒ one semi-skilled = 1/(8×25) = 1/200 of the wall per day.
An unskilled worker: 10 unskilled finish in 30 days ⇒ one unskilled = 1/(10×30) = 1/300 of the wall per day.
Compute the team daily rate by multiplying each per-worker rate by the number of workers and summing:
Team rate = 2×(1/100) + 6×(1/200) + 5×(1/300) = 1/50 + 3/100 + 1/60.
Add the fractions with common denominator 300: 1/50 = 6/300, 3/100 = 9/300, 1/60 = 5/300. Sum = (6+9+5)/300 = 20/300 = 1/15 of the wall per day.
Time to finish = reciprocal of team rate = 15 days.