Question

ays
28. A and B can do a piece of work in 18 days, B and
C can do in 24 days, A and C in 36 days. The time
taken by them to do this work together is
(a) 16 days
(b) 15 days
(c) 12 days
(d) 8 days​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

• (A+B) can do a piece of work in 18 days
• (B+C) can do a piece of work in 24 days.
• (A+C) can do a piece of work in 36 days.

To Find :

• How long they will take to complete work together?

Solution:

Here, given that (A+B), (B+C) and (C+A) are doing a work in 18 days, 24days and 36days respectively.

• Let suppose that total work in 1

Therefore,

• (A+B)'s one day work = 1/18
• (B+C)'s one day work = 1/24
• (C+A)'s one day work = 1/36

Now,

We found that (A+B),(B+C) and (C+A) can do 1/18,1/24 and 1/36 work in one day.

Let find that how much work they will do together in one day :-

⟹ (A+B) +(B+C) + (C+A) one day's work = $\large{\sf{\dfrac{1}{18}+\dfrac{1}{24}+\dfrac{1}{36}}}$

⟹ 2(A+B+C) one day's work = $\large{\sf{\dfrac{4 + 3 + 2}{72}}}$

⟹ 2(A+B+C) one day's work = $\large{\sf{\dfrac{9}{72}}}$

⟹ 2(A+B+C) one day's work = $\large{\sf{\dfrac{1}{8}}}$

⟹ (A+B+C) one day's work = $\large{\sf{\dfrac{1}{8×2}}}$

⟹ (A+B+C) one day's work = $\large{\sf{\dfrac{1}{16}}}$

Now,

We found that A,B and C together can do 1/16 of total work in 1 day where total work is 1[we have supposed]

Therefore,

⟹ Time taken by (A+B+C) together = $\large{\sf{\dfrac{1}{\dfrac{1}{16}}}}$

⟹ Time taken by (A+B+C) together = 1×16

⟹ Time taken by (A+B+C) together = 16days[Option 'A']

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