Question

the value of a car purchased two years ago depreciated at the annual Rate of 10 percent. if it's present value is rs 80000 find
its value after 2 years
original value before 2 years​

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The value of a car purchased two years ago depreciated at the annual rate of 10%. If it's present value is Rs.80000.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The value of after 2 years and before 2 years.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

$\underline{\large{\mathcal{FIRST\:CASE\::}}}$(After 2 years)

• Principal, (P) = Rs.80000
• Rate, (R) = 10%
• Time, (n) = 2 years

We know that formula use :

$\boxed{\bf{Amount=principal\bigg(1-\frac{R}{100} \bigg)^{n} }}}}$

$\dashrightarrow\sf{A=80000\bigg(1-\dfrac{1\cancel{0}}{10\cancel{0}} \bigg)^{2} }\\\\\\\dashrightarrow\sf{A=80000\bigg(1-\dfrac{1}{10} \bigg)^{2} }\\\\\\\dashrightarrow\sf{A=80000\bigg(\dfrac{10-1}{10} \bigg)^{2} }\\\\\\\dashrightarrow\sf{A=80000\bigg(\dfrac{9}{10} \bigg)^{2} }\\\\\\\dashrightarrow\sf{A=80000\times \dfrac{9}{10} \times \dfrac{9}{10} }\\\\\\\dashrightarrow\sf{A=800\cancel{00}\times \dfrac{81}{\cancel{100}} }\\\\\\\dashrightarrow\sf{A=Rs.(800\times 81)}$

$\dashrightarrow\sf{\purple{A=Rs.64800}}$

Thus;

The value of car after 2 years will be Rs.64800 .

$\underline{\large{\mathcal{SECOND\:CASE\::}}}$ (Before 2 years)

$\dashrightarrow\sf{A=\dfrac{80000}{\bigg(1-\dfrac{10}{100} \bigg)^{2} }} \\\\\\\dashrightarrow\sf{A=\dfrac{80000}{\bigg(\dfrac{100-10}{100} \bigg)^{2} }}\\\\\\\dashrightarrow\sf{A=\dfrac{80000}{\bigg(\dfrac{9\cancel{0}}{10\cancel{0}} \bigg)^{2} }}\\\\\\\dashrightarrow\sf{A=\dfrac{80000}{\bigg(\dfrac{9}{10} \bigg)^{2} }} \\\\\\\dashrightarrow\sf{A=\dfrac{80000}{\dfrac{81}{100}}}\\\\\\\dashrightarrow\sf{A=\dfrac{80000}{81} \times 100}\\\\\\\dashrightarrow\sf{A={\dfrac{8000000}{81} }}$

$\dashrightarrow\sf{\purple{A=Rs.98765.43}}$

Thus;

The value of car before 2 years was Rs.98765.43 .

Answer 2

Answer:

• Depreciation : Depreciatie (Decrease) in the value of Asset, Like Here Car.
• As we have to Find Value After 2 years, we will Decrease the Rate of Depreciation according to Number of Year from the Principal.

$\underline{\bigstar\:\boldsymbol{Value\:After\:2\:Years :}}$

$:\implies\sf Amount=Principal\times(100-Depreciation)\%\times(100-Depreciation)\%\\\\\\:\implies\sf Amount=Principal \times \bigg\lgroup\dfrac{100 - Rate}{100}\bigg\rgroup \times \bigg\lgroup\dfrac{100 - Rate}{100}\bigg\rgroup\\\\\\:\implies\sf Amount=80000 \times \bigg\lgroup\dfrac{100 - 10}{100}\bigg\rgroup \times \bigg\lgroup\dfrac{100 - 10}{100}\bigg\rgroup\\\\\\:\implies\sf Amount = 8 \times 90 \times 90\\\\\\:\implies\underline{\boxed{\textsf{Amount = Rs. 64,800}}}$

⠀

$\therefore\:\underline{\textsf{Value of car after 2 years will be \textbf{Rs. 64,800}}}.$

$\rule{170}{2}$

• In this case, we get Principal after depreciating from last two years.
• That's why we will Decrease the Deprecated Rate from following Amount to get our Principal.

$\underline{\bigstar\:\boldsymbol{Value\: Before\:2\:Years :}}$

$:\implies\sf Amount\times(100-Depreciation)\%\times(100-Depreciation)\%=Principal\\\\\\:\implies\sf Amount \times \bigg\lgroup\dfrac{100 - Rate}{100}\bigg\rgroup \times \bigg\lgroup\dfrac{100 - Rate}{100}\bigg\rgroup=Principal\\\\\\:\implies\sf Amount \times \bigg\lgroup\dfrac{100 - 10}{100}\bigg\rgroup \times \bigg\lgroup\dfrac{100 - 10}{100}\bigg\rgroup=80000\\\\\\:\implies\sf Amount \times\dfrac{90}{100} \times\dfrac{90}{100}=80000\\\\\\:\implies\sf Amount = 80000 \times \dfrac{100}{90} \times \dfrac{100}{90} \\\\\\:\implies\underline{\boxed{\textsf{Amount = Rs. 98,765.43}}}$

⠀

$\therefore\:\underline{\textsf{Value of car before 2 years was \textbf{Rs. 98,765.43}}}.$