Question

A and B can dona piece of work in 30 days B and C in 24 days C and A in 40 days how long will it take them to do the work together ​

Answer 1

Answer:

20 days

Step-by-step explanation:

Given : A and B can do a piece of work in 40 days, B and C in 30 days and C and A in 24 days. To find : In what time can each finish it working alone? Together they take A+B+C= 20 days.

Answer 2

$\huge{\underline{\underline{\sf{Answer :-}}}}$

☞A and B can do a piece of work in = 40 days

☞B and C can do a piece of work in = 30 days

C and A can do a piece of work in = 24 days

➠(A+B)’s 1 day work = 1/40

➠(B+C)’s 1 day work = 1/30

➠(C+A)’s 1 day work = 1/24

So, [(A+B)+(B+C)+(C+A)]’s 1 day work = 1/40 + 1/30 + 1/24= (3 + 4 + 5)/120= 12/120 = 1/10

i.e. (A + B + B + C + C + A)’s 1 day work = 1/10

i.e. 2(A + B + C)’s 1 day work = 1/10

∴ (A + B + C)’s 1 day work = 1/20

∴ (A + B + C) can do the work in = 20 days

A’s 1 day work = 1/20 – 1/30= (3 – 2)/60 = 1/60

∴ A can do the work in 60 days

B’s 1 day work = 1/20 – 1/24= (6 – 5)/120 = 1/120

∴ B can do the work in 120 days

Now, C’s 1 day work = 1/20 – 1/40= (2 – 1)/40 = 1/40

∴ C can do the work in 40 days