SOLUTION: A labourer is engaged for 20 days on the condition that he will receive Rs.80 for each day he works and will be fined Rs.6 for each day he is absent. If he receive Rs.826 in all, h

Question 682162: A labourer is engaged for 20 days on the condition that he will receive Rs.80 for each day he works and will be fined Rs.6 for each day he is absent. If he receive Rs.826 in all, how many days did he remain absent.?
Found 2 solutions by stanbon, vidya p:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A labourer is engaged for 20 days on the condition that he will receive Rs.80 for each day he works and will be fined Rs.6 for each day he is absent. If he receive Rs.826 in all, how many days did he remain absent.?
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Equations:
Days Eq: w + a = 20
Value Eq:80w -6a = 826
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Multiply thru the Days Eq. by 80:
80w + 80a = 80*20
80w - 6a = 826
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Subtract and solve for "a";
86a = 774
a = 9 (# of days absent)
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Cheers,
Stan H.
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Answer by vidya p(12) (Show Source): You can put this solution on YOUR website!
This question is related to simultaneous linear equations in two variables.
Solution:
Let x be the number of working days
and y be the number of absent days.
since total number of days are 20 ,
hence we get: x + y = 20
now second condition says
cost for working days is $80 , hence total cost is 80x
cost reduced for absent days is $ 6 ,
hence total cost reduced is 6y
now total amount obtained is $ 826
therefore the equation is: 80x - 6y = 826
now we can solve by elimination method:
x + y = 20 multiply by 6
we get 6x + 6y = 120
and 80x -6y = 826
now add both the equation we get :
86x = 946
x = 946/86
x = 11
plug x = 11 in first equation and get y?
x + y = 20
11 + y = 20
y = 9
hence 11 are working days
and so he remain absent for 9 days.
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