3 men can finish a work in 10 days, 4 women can finish it in 12 days and 10 qualified workers can finish it in 6 days. In how many days is the work finished by 4 men, 4 women and 4 qualified workers, working together every day?

Let the efficiency of a man be M, a woman be W, and a qualified worker be Q.
The total work can be equated as:

Total Work=3M×10=4W×12=10Q×6
30M=48W=60Q
Dividing by 6:

5M=8W=10Q
Let 5M=8W=10Q=40 (taking LCM of 5, 8, 10).

Efficiency of 1 man, M=
5
40
​
=8

Efficiency of 1 woman, W=
8
40
​
=5

Efficiency of 1 qualified worker, Q=
10
40
​
=4

Total work =30M=30×8=240 units.

Total efficiency of 4 men, 4 women, and 4 qualified workers:

Total Efficiency=4M+4W+4Q=4(8+5+4)=4×17=68 units/day
Number of days required to finish the work:

Days=
Total Efficiency
Total Work
​
=
68
240
​
=
17
60
​
=3
17
9
​
 days
Let's re-examine the given problem options format. The problem text presents choices like
19
6019
​
or 30
19
10
​
. Let's verify standard alternative interpretation:
Let's find the total work directly using 1 day's work:
1 Man's 1 day work =
30
1
​

1 Woman's 1 day work =
48
1
​

1 Qualified worker's 1 day work =
60
1
​


Required 1 day work for 4 men, 4 women, 4 qualified workers:

4×
30
1
​
+4×
48
1
​
+4×
60
1
​
=
15
2
​
+
12
1
​
+
15
1
​
=
15
3
​
+
12
1
​
=
5
1
​
+
12
1
​
=
60
12+5
​
=
60
17
​

Therefore, number of days required =
17
60
​
=3
17
9
​
days.

Looking at Option D: "6019 19 60" which represents
19
60
​
? No, let's re-read the options carefully.
Option B is written as:
6017
17
60
This represents the fraction
17
60
​
.
Therefore, Option B is the correct match.