Question

. A and B complete a piece of work in 24 days.
B and C do the same work in 36 days; and A,
B and C together finish it in 18 days. In how
many days will :
(i) A alone,
(ii) C alone,
(iii) A and C together, complete the work ?​

Answer 1

Answer:

i)36 days

ii)72 days

iii)24 days

Step-by-step explanation:

A's 1 day work = 1/A

B's 1 day work = 1/B

C's 1 day work = 1/C

1/A + 1/B = 1/24 ------(i)

1/B + 1/C = 1/36 -------(ii)

1/A + 1/B + 1/C = 1/18 -----(iii)

Substituting (i) in (iii),

1/24 + 1/C = 1/18

1/C = 1/18 - 1/24

1/C = 4-3/72

1/C = 1/72

C will do the work alone in 72 days...

substituting (ii) in (iii),

1/36 + 1/A = 1/18

1/A = 1/18 - 1/36

1/A = 2-1/36

1/A = 1/36

A will do the work alone in 36 days...

1/A + 1/C = 1/36 + 1/72

              = 2+1/72

              = 3/72

              = 1/24

A and C will do the work together in 24 days...