The value of a machine depreciates at the rate of 10% p.a. At the end of 4 years, its value becomes Rs. 1,31,220. Find the original value.
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Step-by-step explanation:
Let the value of the machine, at the onset, be x when x is in Rs.
Here we shall apply the rule
Final value = original value ×(1+rate)
time
.
Here the rate will be negative since the value is depriciating.
For two yrs. the rate of depriciation is 10%.
∴ the value after 2 yrs.
= x×(1−
100
10
)
2
=x×
10
9
×
10
9
.
As given, the rate of depriciation for next 2 yrs =5%
∴ The value after next 2 yrs
= x×
10
9
×
10
9
×(1−
100
5
)
2
=x×
10
9
×
10
9
×
20
19
×
20
19
But the final value after 4 yrs = Rs. 146205.
∴x×
10
9
×
10
9
×
20
19
×
20
19
=146205
⇒x=
81×19×19
146205×40000
=5×40000
⇒x= Rs. 200000.
So, 4 yrs. back, the value of the machine was Rs. 200000.
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