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 . In what time they can do it, all working together​

Answer 1

Answer:

• (A + B) = 18 Days
• (B + C) = 24 Days
• (C + A) = 36 Days

Let they altogether can do work in x days.

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

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

⠀

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