21 km road can be done by 45 workers in 300 days. 100 days later only 5 km…
2023
21 km road can be done by 45 workers in 300 days. 100 days later only 5 km road is completed. So how many workers should more join to complete work in same time?
- A.
72
- B.
62
- C.
45
- D.
27
Attempted by 5 students.
Show answer & explanation
Correct answer: D
Key idea: Use the actual work done in the first 100 days to find each worker's daily rate, then compute how many additional workers are needed to finish the remaining work in the remaining 200 days.
Treat the whole job (21 km) as 1 unit. Work done in the first 100 days = 5 km = 5/21 of the job.
One worker's one-day work = (5/21) ÷ (45 workers × 100 days) = (5/21) / 4500 = 1/(21 × 900).
Remaining work = 1 − 5/21 = 16/21.
Let x be the number of additional workers. Then (45 + x) workers working for 200 days do: (45 + x) × 200 × 1/(21 × 900) of the job. Set this equal to 16/21.
Equation: (45 + x) × 200 × 1/(21 × 900) = 16/21. Multiply both sides by 21 and simplify: (45 + x) × 200/(900) = 16 ⇒ (45 + x) × (2/9) = 16.
Solve: 45 + x = 16 × (9/2) = 72, so x = 72 − 45 = 27.
Answer: 27 more workers are required.