Question

A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36 days what time can they do it, all working together?​

Answer 1

Answer:

A+B B+C C+A

18 24 36

72

4 3 2

(A+B+C) = 9/2 =4.5

A=1.5

B=2.5

C=0.5

Total work = 72/4.5 =16days

Answer 2

Answer:

Let they altogether can do work in x days.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf 2(A+B+C)=\dfrac{x}{18}+\dfrac{x}{24}+\dfrac{x}{36}=Work\\\\\\:\implies\sf (A+B+C)=\dfrac{1}{2} \bigg(\dfrac{x}{18}+\dfrac{x}{24}+\dfrac{x}{36} \bigg)=1\\\\\\:\implies\sf \dfrac{1}{2} \bigg(\dfrac{x}{18}+\dfrac{x}{24}+\dfrac{x}{36} \bigg)=1\\\\\\:\implies\sf \dfrac{4x + 3x+2x}{72} = 2\\\\\\:\implies\sf \dfrac{9x}{72} = 2\\\\\\:\implies\sf \dfrac{x}{8} = 2\\\\\\:\implies\sf x = 2 \times 8\\\\\\:\implies\underline{\boxed{\sf x = 16 \:Days}}$

⠀

$\therefore\:\underline{\textsf{In \textbf{16 Days} they can do it working altogether.}}$