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**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 altogether? Also find the number of days taken by each to do the same work, working alone.**

Answer:

Given:

(A + B)’s can build a wall in = 10 day

(A + B)’s 1 day work = 1/10

(B + C)’s can build a wall in = 15 days

(B + C)’s 1 day work = 1/15

(C + A)’s can build a wall in = 12 days

(C + A)’s 1 day work = 1/12

[(A+B) + (B+C) + (C+A)]’s 1 day work = 1/10 + 1/15 + 1/12

2 (A+B+C)’s 1 day work = (6 + 4 + 5)/60

= 15/60

= ¼

(A+B+C)’s 1 day work = 1/(2×4)

= 1/8

So, (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:

=>Also, [(A+B+C) - (B + C)]’s 1 day work = 1/8 – 1/15

= (15 - 8)/120

= 7/120

A’s 1 day work = 7/120

So, A can build the wall in = 120/7 days

= 17 1/7 days

=>Also, [(A+B+C) - (A + C)]’s 1 day work = 1/8 – 1/12

= (3 - 2)/24

= 1/24

B’s 1 day work = 1/24

So, B can build the wall in = 24 days

=>Also, [(A+B+C) - (A + B)]’s 1 day work = 1/8 – 1/10

= (5 - 4)/40

= 1/40

C’s 1 day work = 1/40

So, C can build the wall in = 40 days

∴ A can complete the work in 17 1/7 days.

B can complete the work in 24 days.

C can complete the work in 40 days

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