A work can be finished by 8 men in 10 days working 6 hours a day or same can be finished by 20 qualified workers in 6 days working 8 hours a day. 2 men and 4 qualified workers work simultaneously 10 hours a day, the work will be finished in ________ days.

Given:

A work can be finished by 8 men in 10 days working 6 hours a day or same can be finished by 20 qualified workers in 6 days working 8 hours a day.

2 men and 4 qualified workers work simultaneously 10 hours a day.

Formula used:

Work done = Number of workers × Number of days × Number of hours per day

Calculation:

Work done by 8 men in 10 days working 6 hours/day:

⇒ 8 × 10 × 6 = 480 man-hours

Work done by 20 qualified workers in 6 days working 8 hours/day:

⇒ 20 × 6 × 8 = 960 qualified worker-hours

Assume 1 man-hour = x qualified worker-hours. Then:

⇒ 480 man-hours = 960 qualified worker-hours

⇒ 1 man-hour = 2 qualified worker-hours

2 men working 10 hours/day:

⇒ 2 × 10 = 20 man-hours

⇒ 20 man-hours = 20 × 2 = 40 qualified worker-hours

4 qualified workers working 10 hours/day:

⇒ 4 × 10 = 40 qualified worker-hours

Total work done per day by 2 men and 4 qualified workers:

⇒ 40 + 40 = 80 qualified worker-hours

Total work required in qualified worker-hours:

⇒ 960 qualified worker-hours

Number of days required to finish the work:

⇒ 960 / 80 = 12 days

∴ The correct answer is option (3).