Question

3. A and B can do a piece of work in 18 days.
Band C in 24 days, C and A in 36 days. In
how many days can they do it all working
together?
(a) 16 days
(b) 17 days
(c) 15 days
(d) None of these​

Answer 1

Step-by-step explanation:

A and B do a piece of work in 18 days.

Work done by A and B in 1 day = 1/18

___ (eq 1)

Similarly,

B and C do a piece of work in 24 days & C and A do a piece of work in 32 days.

Work done by B and C in 1 day = 1/24

___ (eq 2)

Work done by C and A in 1 day = 1/36

___ (eq 3)

We have to find that in how manu days they do all complete the work when they work together.

To find in how many days do they all complete the work together we have to add (eq 1), (eq 2) and (eq 3)

So,

=> (A and B) + (B and C) + (C and A) = 1/18 + 1/24 + 1/36

=> A + B + B + C + C + A = (32 + 24 + 16)/576

=> 2A + 2B + 2C = 72/576

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

=> A + B + C = 1/16

•°• In 16 days they complete all the work when they work together.

Option (a) 16 days

Answer 2

Answer :-

It takes 16 days if they all work together i.e Option (a).

Explanation :-

A and B can do a piece of eork in 18 days

So, A and B's 1 day work (A + B) = 1/18

B and C can do it in 24 days

So, B and C's 1 day work (B + C) = 1/24

C and A can do it in 36 days

C and A's 1 day work (C + A) = 1/36

Let the A, B and C's 1 day work be (A + B + C)

By observation :

(A + B) + (B + C) + (C + A) = 2(A + B + C)

By substituting the values

⇒ (1/18) + (1/24) + (1/36) = 2(A + B + C)

Taking LCM

⇒ (4 + 3 + 2)/72 = 2(A + B + C)

⇒ 9/72 = 2(A + B + C)

⇒ 1/8 = 2(A + B + C)

⇒ (1/8) ÷ 2 = A + B + C

⇒ (1/8) * (1/2) = A + B + C

⇒ 1/16 = A + B + C

⇒ A + B + C = 1/16

A, B, C's 1 day work = 1/16

So A, B and C will take 16 days to do the work.

∴ It takes 16 days if they all work together i.e Option (a).