A and B together can build a wall in 10 days B and C working together can do it in 15 days C and A together can do it in 12 days how long will they take to finish the work working on together also for find the number of days taken by each to do the same work working alone
Answers
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.