Rahul purchased a Maruti van for Rs. 1, 96,000 and the rate of depreciation is $$14\frac{2}{7}\% $$ per annum. Find the value of the van after two years.
A. Rs. 1,40,000
B. Rs.1,44,000
C. Rs. 1,50,000
D. Rs. 1,60,000
E. None of these
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Value}}\,{\text{of}}\,{\text{maruti}}\,{\text{Van}},\, \cr & {V_0} = Rs.\,196000 \cr & {\text{Rate}}\,{\text{of}}\,{\text{depreciation}},\, \cr & r = 14 {\frac{2}{7}} \% = \frac{{100}}{7}\% ; \cr & {\text{Time}},\,t = 2\,{\text{years}} \cr & {\text{Let}}\,{V_1}\,{\text{is}}\,{\text{the}}\,{\text{value}}\,{\text{after}}\,{\text{depreciation}}. \cr & {V_1} = {V_0} \times {\left[ {1 - \left( {\frac{r}{{100}}} \right)} \right]^t} \cr & {V_1} = 196000 \times {\left[ {1 - \left( {\frac{{\left( {\frac{{100}}{7}} \right)}}{{100}}} \right)} \right]^2} \cr & {V_1} = 196000 \times {\left( {1 - {\frac{1}{7}}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{7-1}{7}} \right)^2} \cr & {V_1} = 196000 \times {\left( {\frac{6}{7}} \right)^2} \cr & {V_1} = \frac{{\left( {196000 \times 36} \right)}}{{49}} \cr & {V_1} = Rs.\,144000 \cr} $$Join The Discussion
Comments ( 5 )
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How did (6/7)² came some please explain
r= 14(2/7)%
= 100/7 %
= how!!!
I need answer without formula
There was a calculation mistake which is corrected now. Thanks for pointing it out.
how is it calculated?
Value of Maruti Van, V0= Rs. 196000
Rate of depreciation, r = 14(2/7)% = 100/7%; Time, t = 2 years
Let V1 is the value after depreciation.
V1 = V0*[1-(r/100)]t
V1 = 196000*[1-(100/7*100)]2
V1 = 196000*(6/7)2
V1 = (196000*36)/49 = Rs. 144000.