Question

a tv manufacturer reduces the price of a particular model by 10% every year. the current price of this model is 9000.what would be the price after 2 years

Answer 1

Given :

• Current price of TV model = Rs.9000
• It reduces every year = 10 %

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To Find :

• Price of TV after 2 years = ?

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Solution :

~ Formula Used :

$\large{\color{darkblue}{\dashrightarrow}} \: \: {\underline{\overline{\boxed{\red{\sf{ C.I = P \bigg[ 1 + \dfrac{R}{100} \bigg]^n - P }}}}}}$

Where :

• ➙ C.I = Decrease in cost
• ➙ P = Present Cost
• ➙ R = Rate of Decrease
• ➙ n = Time

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~ Calculating the Decrease in cost :

${\longmapsto{\qquad{\sf{ C.I = P \bigg[ 1 + \dfrac{R}{100} \bigg]^n - P }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \bigg[ 1 + \dfrac{10}{100} \bigg]^2 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \bigg[ 1 + \cancel\dfrac{10}{100} \bigg]^2 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \bigg[ 1 + 0.10 \bigg]^2 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \bigg[ 1.10 \bigg]^2 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \times 1.10 \times 1.10 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 9000 \times 1.21 - 9000 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ C.I = 10890 - 9000 }}}} \\ \\ \ {\qquad{\textsf{ Price decrease on the TV model = {\green{\sf{ ₹ \: 1890 }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Price after 2 years :

${:\implies{\qquad{\sf{ Price{\small_{(After \: 2 \: years)}} = Price{\small_{(Present)}} - Decrease \: in \: Price }}}} \\ \\ \ {:\implies{\qquad{\sf{ Price{\small_{(After \: 2 \: years)}} = 9000 - 1890 }}}} \\ \\ \ {\qquad{\textsf{ Price of the TV after 2 years = {\orange{\sf{ ₹ \: 7110 }}}}}}$

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Therefore :

❝ Price of the TV model after 2 years will be ₹ 7110 . ❞

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Answer 2

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{ Question :-}}}}}}}}}$

A tv manufacturer reduces the price of a particular model by 10% every year. the current price of this model is 9000.what would be the price after 2 years.

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{ Given :-}}}}}}}}}$

• CURRENT PRICE OF TV MODEL = Rs. 9,000
• THE PRICE REDUCES EVERY YEAR BY 10%.

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{ To \: Find :-}}}}}}}}}$

• PRICE OF TV AFTER 2 YEARS.

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{ Formula \: Used :-}}}}}}}}}$

$⟼ \: C.I = P[1 + \frac{R}{100} ]^{n} - P$

WHERE;

• ⟼ C.I = DECREASE IN COST.

• ⟼ P = PRESENT COST.

• ⟼ R = RATE OF DECREASE.

• ⟼ N = TIME.

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{  Solution :-}}}}}}}}}$

THE DECREASE IN COST =

$⟼ \: C.I = P[1 + \frac{R}{100} ]^{n} - P$

$⟼ \: C.I = \: 9000[1 + \frac{10}{100} ]^{2} - 9000$

$⟼ \: C.I = 9000[1 + 0.10]^{2} - 9000$

$⟼ \: C.I = 9000[1.10]^{2} - 9000$

$⟼ \: C.I = 9000 \times 1.10 \times 1.10 - 9000$

$⟼ \: C.I = 9000 \times 1.21 - 9000$

$⟼ \: C.I = 10890 - 9000$

$⟼ \: C.I = 1890$

THE DECREASE IN COST = Rs. 1890

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{  Therefore :-}}}}}}}}}$

THE PRICE AFTER 2 YEARS =

⟹ PRICE (AFTER 2 YEARS) = PRICE (PRESENT) - DECREASE IN PRICE

⟹ PRICE (AFTER 2 YEARS) = Rs. (9000 - 1890)

⟹ PRICE (AFTER 2 YEARS) = Rs. 7110

$\large{\blue{\maltese \: \: {\pink{\underbrace{\underline{\red{\pmb{\sf{  Answer :-}}}}}}}}}$

THE PRICE OF THE TV AFTER 2 YEARS IS Rs. 7110.