Question

the value of a car decreases annually by 20%. If the present value of the car be rs 450000, what will be its value after 2 years?​

Answer 1

Given :-

• Value of car decreases annually 20%

• Present value of car is Rs 450000

To find :-

• The value of car after 2 years

Formula :-

Formula of depreciation is as follows :-

$\underline{ \underline{ \sf {\implies \: V \: = V_0(1 - \frac{R}{100})^{n} }}}$

• $\sf{ R \:=\: rate \: of \: depreciation\: per \: year}$

• $\sf{ n\:=\: time \: period}$

• $\sf{V_0 \:=\: present\: value \: of \: car}$

• $\sf{V \:=\: value\: after \: n\: years}$

Now putting values in this formula

$\sf{ \implies \: 450000( {1 - \frac{20}{100}) }^{2} }$

$\sf{ \implies 450000{\frac{100-20}{100}}^{2} }$

$\sf {\implies \: 450000( { \frac{80}{10} })^{2} }$

$\sf{\implies 45000 (\frac{80 \times 80}{100 \times 100}) }$

$\sf {\implies \: 45 \times 80 \times 80}$

${\underline{\underline{\sf{\implies 288000 \: will\: be \: value\: of \: car \: after \: 2 \: years}}}}$

Answer 2

✎ Given :-

• Reduction Percentage = 20%

• Present value of car = 450000

✎ To Find :-

• Value of car after 2 years

✎ Solution :-

Now,

➥ Reduction of Price of Car in 1st year :-

↣ 450000 × 20/100 = 450000 × 0.2 = 90,000

↣ Price reduced during 1st year = 90,000

Now,

↣ Price of Car after 1 year = 4,50,000 - 90,000 = 3,60,000

Now,

➥ Price reduced during 2nd year :-

↣ 360000 × 20/100 = 360000 × 0.2 = 72,000

↣ Price of car reduced = 72,000

Hence,

➥ Value of Car after 2 years = 360000 - 72000 = 2,88,000