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The average monthly salary of 660 workers in a factory is Rs. 380. The average monthly salary of officers is Rs. 2100 and the average monthly salary of the other workers is Rs. 340. Find the number of other workers.
Answer & Solution
Correct Answer:
Option
A
$$\eqalign{
& {\text{Total}}\,{\text{salary}}\,{\text{of}}\,660\,{\text{workers}} \cr
& = 660 \times 380 \cr
& = Rs.\,250800 \cr
& {\text{If}}\,{\text{other}}\,{\text{workers}}\,{\text{be}}\,x;\,{\text{then}}, \cr
& = \left[ {\left( {660 - x} \right) \times 2100} \right] + 340x \cr
& = 250800 \cr
& Or,\,1386000 - 2100x + 340x = 250800 \cr
& 1760x = 1135200 \cr
& {\text{Hence}},\,x = \frac{{1135200}}{{1760}} = 645 \cr
& {\text{Number}}\,{\text{of}}\,{\text{other}}\,{\text{workers}} = 645 \cr} $$
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LoginTotal money - spending money
380 - 340 =40
Then
a)660×40= 26400
b)2100-340= 1760
a-b = 15
Then ,
660-15 =645
If I given avg salary all workers(spend money) =(340×660)
Total money=(660×380)
Than total money - spend money= some money left.
{660×380- 660×340) =(660×40)
Than nums of officers = 660×40/2100-340
= 660×30/1760
=15
Total number of others workers =660-15 645 .
For no. of officers = 660× (380-340 )/2100-340
380-340=40(let no. Of other worker y)
Then 1720x-40y=0
1720x=40y
x/y=1/43
Total worker be 43a+1a=44a
a=660/44=15
No. Of other worker is 15×43=645
Therefore no.of officers = 660-x
Salary of workers = 340 * x
& Salary of officers = 2100 * (660-x)
Now,
Total salay = 660*380
Total salay = salary of officers+ salary of workers
(660*380)= (2100*(660-x))+340x
250800=1386000-2100x+340x
1760x=1135200
X=1135200/1760
Therefore, x= 645
Total Salary of wrkrs=660x380=250800
Let x be the no. Of other workers, then put values of averages respectively in above mentioned formula.
340=Total Salary of other wrkrz / x
Total salary of other wrkrz= 340x
Now, for officers
2100 =Total salary of officers / 660-x
Total salary of officers =2100(660-x)
Since we know that;
Total salary of workers = Total salary of Officers + Total salary of other workers
250800 = 2100(660-x) + 340x
250800 = 1386000-2100x+340x
250800 - 1386000 = -2100x + 340x
-1135200 = -1760x
645 = x