A computer purchased for ₹72900 loses two-third of its value every year. Its value is evaluated at the end of every year. (1) Which of the following expressions gives the value of the computer (in ₹) after n years? 1. 2. 3. 4. (2) Find the value of the computer after 3 years. 1. ₹8100 2. ₹2430 3. ₹5600 4. ₹2700 (3) In how many years will the value of the computer be less than ₹200 ? 1. 6 years 2. 7 years 3. 8 years 4. 10 years (4) By how much will the value of the computer reduce in 4 years ? 1. ₹24300 2. ₹1800 3. ₹8100 4. ₹72000

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KnowledgeBoat · Accepted Answer

(1) Given: Initial Value = ₹72,900 Loss in value every year = Value remaining every year = of the previous year's value. Every year, the value is multiplied by . After n years, the value is , which is . Hence, option 3 is the correct option. (2) Value of the computer after 3 years = ? Value of the computer after n years = [From previous step] By replacing the value of 'n' with 3, we get: ₹ = ₹2700 Hence, option 4 is the correct option. (3) We know at 3 years, value = ₹2700. [From previous step] Value remaining every year = of the previous year's value. [From step 1] ∴ Value after 4 years = Value after 5 years = Value after 6 years = Since 100 200, it takes 6 years. Hence, option 1 is the correct option. (4) Value of the computer reduced in 4 years = ? Value after 4 years = ₹ Value of the computer reduced in 4 years = Initial value - Value after 4 years Substituting the values in above, we get: Value of the computer reduced in 4 years = ₹72900 - ₹ 900 = ₹ 72000 Hence, option 4 is the correct option.

Mathematics

Exponents

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