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 workers = W
No: of 4 legged chairs = W = No: of 4 legged tables
No: of 3 legged stools = No: of 4 legged almirahs
No: of stools = W + 1
Given, total legs = 585
2*W + 4*W + 4*W + 3*(W+1) + 4*(W+1) = 585...
[2*W=worker's leg count, 4*w = chair's legs, 4*W = table's legs, 3*(W+1) = stool' legs, 4*(W+1)= almirah's]
17*W + 7 = 585
17W = 578
W = 34
No: of members in office = 34
Hope it helps

Answer 2

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

Correct option is (b) 34

 Given :-

4 legged chairs = 4 legged tables = no of workers .

3 legged stools = 4 legged almirahs

No. of stools = 1 + no. of workers

Total no. of legs = 585

Solution :

Let the no. of workers = x

$2x + x * 4 + x * 4 + ( x + 1 ) 3 + ( x + 1 )4 = 585\\2 x + 4x + 4x + 7x + 7 = 585\\17 x = 578\\x = 34$

Hence , the no. of workers are 34 .

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