Question

13. A and B can do a piece of work in 20 days, B and C in 30 days and C and A in 36 days.
(i) How much time will it take to finish the work together?
(ii) In how many days, will each finish the work alone?

it answer should be
18 days
45,36,180 days​

Answer 1

Step-by-step explanation:

A+ B can do a work in 20 days.

therefore in 1 day they complete 1/20th work

B+ C can do a work in 30 days.

therefore in 1 day they complete 1/30th work

C+ A can do a work in 36 days.

therefore in 1 day they complete 1/36th work

i) if they work together in one day they will complete

(A+B)+(B+C)+(C+A) = (1/20) + (1/30) + (1/36)

➡2A +2B + 2C = (1/20) + (1/30) + (1/36)

➡2(A+B+C) = (27+18+15)/ 540 { here we took 2 as common and also 540 is the LCM of 20,30&36}

➡2(A+B+C) = 60/540

➡2(A+B+C) = 1/9

➡A+B+C = 1/(9×2)

➡A+B+C = 1/18

since they together complete 1/18 th of the work in one day so they will need 18 days to complete the work.

ii) A+ B+ C = 1/18

➡A + (B+C) = 1/18

➡A + 1/30 = 1/18

➡A = (1/18) - (1/30)

➡A = (5-3)/ 90 {here we took LCM of 18 & 30}

➡A = 2/90

➡A =1/45

Since A complete 1/45th of the work in one day so A will complete tge whole work in 45 days.

similarly ,

A+B+C =1/18

➡B + (C+A) = 1/18

➡B + 1/36 = 1/18

➡B = (1/18) - (1/36)

➡B = (2-1)/36

➡B = 1/36

so B will complete the work in 36 days.

A+B+C =1/18

➡C + (A+B) = 1/18

➡C + 1/20 = 1/18

➡C = (1/18) - (1/20)

➡C = (10-9)/180

➡C = 1/180

So C will complete the work in 180 days