Question

A and B can do a peace of work in 18 days, B and C in 24 days, A and C in 36 days in what time can they do it all working together

Answer 1

16 days

(A + B)’s 1 day’s work = \frac{1}{18}

(B + C)’s 1 day’s work = \frac{1}{24}

(C + A)’s 1 day’s work = \frac{1}{36}

On adding,

2(A + B + C)’s 1 day’s work = \frac{1}{18}+\frac{1}{24}+\frac{1}{36} = \frac{4+3+2}{72} = \frac{1}{8}

∴ (A + B + C)’s 1 day’s work = \frac{1}{16}

∴ A, B and C together will complete the work in 16 days.

Answer 2

A and B = 18 days

B and C = 24 days

A and C = 36 days

1 day work of A+B = 1/18

1 day work of B+C = 1/24

1 day work of A+C = 1/36

Adding,

A+B+B+C+A+C = 1/18 + 1/ 24 + 1/36

2(A+B+C) = (4+3+2) / 72 = 9/72 = 1/8

2(A+B+C) = 1/8

A+B+C = 1/16

1 day work of ABC together is 1/16 so,

They all together will be able to do it in 16 days.