X, Y and Z can complete a piece of work in 8, 20 and 25 days respectively. Working together, they will complete the same work in:
- A43
180
days - B43
162
days - C43
200
days - D43
172
days
Solution & Step-by-step Explanation
Work done by X in 1 day =
8
1
Work done by Y in 1 day =
20
1
Work done by Z in 1 day =
25
1
Total work done by X, Y, and Z together in 1 day is:
8
1
+
20
1
+
25
1
Find the LCM of denominators 8, 20, and 25:
LCM(8,20,25)=200
Now convert the fractions:
200
25+10+8
=
200
43
Since they do
200
43
of the work in 1 day, the total number of days taken to complete the entire work together is the reciprocal:
Total Days=
43
200
days
8
1
Work done by Y in 1 day =
20
1
Work done by Z in 1 day =
25
1
Total work done by X, Y, and Z together in 1 day is:
8
1
+
20
1
+
25
1
Find the LCM of denominators 8, 20, and 25:
LCM(8,20,25)=200
Now convert the fractions:
200
25+10+8
=
200
43
Since they do
200
43
of the work in 1 day, the total number of days taken to complete the entire work together is the reciprocal:
Total Days=
43
200
days