Question

An office has as many four legged chairs and as many four legged tables as workers and as many three legged stools as four legged almirahs. If the number of stools be one more than the number of workers and total number of legs be 585. The numbers of members in the office are

(a) 17
(b) 34
(c) 16
(d) Cannot be determined

Answer 1

Let the number of 4-legged chairs be x.
Number of 4-legged tables = 4-legged chairs = x
Number of workers = Number of 4-legged tables = Number of 4-legged chairs = x

Let the number of 3-legged stools be y.
Number of 4-legged almirahs = y

We are given number of stools, y = number of workers + 1 = x + 1
Thus, number of 3-legged stools = number of 4-legged almirahs = x + 1

Total legs given = 585

Therefore,
$$\begin{gathered} 4x+4x+2x+3\left(x+1\right)+4\left(x+1\right)=585 \\ \Rightarrow 10x+3x+3+4x+4=585 \\ \Rightarrow 17x+7=585 \\ \Rightarrow 17x=578 \\ \Rightarrow x=34 \end{gathered}$$

Thus, number of members or workers in the office, x = 34 (answer)