10. A, B and C can together construct a well in 4 days. A alone can construct the well in 12 days and Balone can construct the well in 10 days, How much time will C take to construct the well? solve it
Answers
Answer:
Step-by-step explanation:
Given,
(A+B)’s can build a wall in = 10 day
So, (A+B)’s 1 day's work =1/10
(B+C)’s can build a wall in =15 days
So, (B+C)’s 1 day's work =1/15
(C+A)’s can build a wall in =12 days
So, (C+A)’s 1 day's work =1/12
∴[(A+B)+(B+C)+(C+A)]’s 1 day work =
10
1
+
15
1
+
12
1
=
60
6+4+5
=
60
15
=
4
1
⇒2(A+B+C)’s 1 day's work =
4
1
⇒(A+B+C)’s 1 day's work =
2
1
×
4
1
=
8
1
Hence, (A+B+C) can build the wall in =8 days
Now let us find the number of days taken by each to do the same work, working alone:
[(A+B+C)−(B+C)]’s 1 day work =
8
1
−
15
1
=
120
15−8
=
120
7
⇒A’s 1 day work =
120
7
So, A can build the wall in =
7
120
days =17
7
1
days
Again, [(A+B+C)−(A+C)]’s 1 day's work =
8
1
−
12
1
=
24
3−2
=
24
1
⇒B’s 1 day's work =
24
1
So, B can build the wall in =24 days
Again, [(A+B+C)–(A+B)]’s 1 day work =
8
1
−
10
1
=
40
5−4
=
40
1
⇒C’s 1 day's work =
40
1
So, C can build the wall in =40 days
∴ A can complete the work in 17
7
1
days.
B can complete the work in 24 days.
C can complete the work in 40 days.