Question

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

Answer 1

Answer:

38 days.....................

Answer 2

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