Question

2. A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can
finish it in 36 days. In how many days can A, B, C finish it, if they all work together?​

Answer 1

Required Answer:-

Given:-

• A and B can finish work in 18 days.

• B and C can finish work in 24 days.

• A and C can finish work in 36 days.

To find:-

• Days in which A, B and C can finish work in.

Solution:-

We have,

A and B can finish work in = 18 days,

$\sf \footnotesize{ \therefore( \: A \: + \: B \:)one \: day \: work \: = \: \frac{1}{18} \: \: \: \: \: \: \: \: \: \: \: - (i)}$

$\sf \footnotesize{similarly , (B \: + \: C) \: one \: day \: work \: = \: \frac{1}{24} \: \: \: \: \: \: \: \: \: \: \: - (ii) }$

$\sf \footnotesize{and , (A \: + \: C) \: one \: day \: work \: \: = \: \frac{1}{36} \: \: \: \: \: \: \: \: \: \: \: - (iii) }$

Now, adding (i), (ii), and (iii), we get,

$\sf \footnotesize{(A + B + B + C + A + C) \: one \: day \: work \: = \: \frac{1}{18} + \frac{1}{24} + \frac{1}{36} = \frac{9}{72} = \frac{1}{8} }$

$\sf \footnotesize{2(A + B +C) \: one \: day \: work \: = \: \frac{1}{8} }$

$\sf \footnotesize{(A + B + C) \: one \: day \: work \: = \: \frac{1}{8 \times 2} = \frac{1}{16} }$

$\sf \footnotesize{Hence, \: they \: can \: finish \: work \: in \: = \: 16 \: days}$

Hence, they all three can finish work in 16 days.