If 33 untrained labourers can do a work in 15 days of 12 hr. each, how many…
2023
If 33 untrained labourers can do a work in 15 days of 12 hr. each, how many trained labourers can do 50% more work in 11 days of 9 hr each ? (It may be assumed that it takes 2 trained labourers to do the work of 5 untrained labourers)
- A.
42
- B.
36
- C.
90
- D.
100
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Key idea: convert all work into untrained-equivalent man-hours, using the given trained-to-untrained equivalence.
Find the equivalence: two trained labourers do the work of five untrained labourers, so one trained labourer = 5/2 = 2.5 untrained labourers.
Compute total untrained-equivalent man-hours for the original work: 33 untrained × 15 days × 12 hours/day = 33 × 180 = 5940 untrained-hours.
Required work is 50% more, so required untrained-equivalent hours = 1.5 × 5940 = 8910 untrained-hours.
Each trained labourer supplies in the given period: 11 days × 9 hours/day × 2.5 (untrained-equivalent per trained) = 11 × 9 × 2.5 = 247.5 untrained-hours.
Number of trained labourers needed = total required untrained-hours ÷ untrained-hours per trained = 8910 ÷ 247.5 = 36.
Answer: 36 trained labourers are required.