The value of a machine worth ₹5,00,000 depreciates at the rate of 10% every year. In how many years will its value be ₹3,64,500?
27jenny:
ur ans is 3 years
Answers
Answered by
46
Solution :
Value of a machine = Rs 500000
rate of depreciation (d) = 10%
Let n in ' n ' years it becomes
Rs 364500 .
364500 = 500000 ( 1 - 10/100 )ⁿ
=> (364500/500000 ) = ( 1 - 1/10 )ⁿ
=> 0.729 =[ ( 10 - 1 )/10]ⁿ
=> ( 729/1000 ) = (9/10)ⁿ
=> ( 9³/10³ ) = ( 9/10 )ⁿ
=> ( 9/10 )³ = ( 9/10 )ⁿ
Therefore ,
n = 3
[ Since , if a^m = a^n then m = n ]
In " 3 " years the value of machine
becomes Rs364500 .
••••
Value of a machine = Rs 500000
rate of depreciation (d) = 10%
Let n in ' n ' years it becomes
Rs 364500 .
364500 = 500000 ( 1 - 10/100 )ⁿ
=> (364500/500000 ) = ( 1 - 1/10 )ⁿ
=> 0.729 =[ ( 10 - 1 )/10]ⁿ
=> ( 729/1000 ) = (9/10)ⁿ
=> ( 9³/10³ ) = ( 9/10 )ⁿ
=> ( 9/10 )³ = ( 9/10 )ⁿ
Therefore ,
n = 3
[ Since , if a^m = a^n then m = n ]
In " 3 " years the value of machine
becomes Rs364500 .
••••
Answered by
8
Answer:Solution :
Value of a machine = Rs 500000
rate of depreciation (d) = 10%
Let n in ' n ' years it becomes
Rs 364500 .
364500 = 500000 ( 1 - 10/100 )ⁿ
=> (364500/500000 ) = ( 1 - 1/10 )ⁿ
=> 0.729 =[ ( 10 - 1 )/10]ⁿ
=> ( 729/1000 ) = (9/10)ⁿ
=> ( 9³/10³ ) = ( 9/10 )ⁿ
=> ( 9/10 )³ = ( 9/10 )ⁿ
Therefore ,
n = 3
[ Since , if a^m = a^n then m = n ]
In " 3 " years the value of machine
becomes Rs364500
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