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Ajay had purchased a second-hand scooter for Rs. 18000 and spent Rs. 1800 for repairs. After 1 year he wanted to sell the scooter. At what price should he sell it to gain $\dfrac{100}{9}$%, if $\dfrac{100}{11}$% is to be deducted at the end of every year on account of depreciation?
A. 10000
B. 20000
C. 30000
D. 40000

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: Ajay spends in total the price of the scooter and its repair cost. We find the total cost. Then we find the depreciated value of the scooter after 1 year. Ajay wants to make a profit of $\dfrac{100}{9}$% on that value. We find the final selling price of the scooter.

Complete step by step answer:
Ajay had purchased a second-hand scooter for Rs. 18000 and spent Rs. 1800 for repairs.
So, the total amount he spends on the scooter is Rs. $18000+1800=19800$.
The depreciation is the representation of how much of an asset's value has been used up.
So, the value of the scooter will get less by $\dfrac{100}{11}$% per year.
At the end of the first year the price of the scooter will be less by $\dfrac{100}{11}$% of 19800.
So, the price of the scooter after 1 year will be
$19800\left( 1-\dfrac{100}{11\times 100} \right)=\dfrac{19800\times 10}{11}=18000$ Rs.
So, the current price when Ajay is trying to sell the scooter is 18000. He wants to make a gain $\dfrac{100}{9}$%. So, he has to sell the scooter at the price of
$18000\left( 1+\dfrac{100}{9\times 100} \right)=\dfrac{18000\times 10}{9}=20000$ Rs.
Ajay has to sell the scooter at a price of Rs. 20000.

So, the correct answer is “Option B”.

Note: We first need to remember, for Ajay the profit will not just be on the cost of the scooter as it will be on the total value consisting the cost of the scooter and the repair. The account of depreciation acts in the same way.