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# Archana wants to buy a TV that costs Rs. 19,000 but she has only Rs. 15,000. So she decides to invest her money at 8% simple interest per year. After how many years, will she be able to buy the TV?

Last updated date: 20th Mar 2023
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Hint: Let us go through by the formula of simple interest that we study in the chapter of simple interest i.e., $SI = \dfrac{{P \times R \times T}}{{100}}$ . By this formula we will be able to calculate time because we will find the interest by subtracting money she has from the cost price of TV.

Here in the question it is given that Archana has only Rs. 15,000.
And she wants to buy a TV that costs Rs. 19,000.
So the extra amount she needs as a simple interest is (cost price of TV- the money she has).
I.e. SI=19000-15000=Rs. 4000.

So, she needs Rs. 4000 extra as simple interest.
We have to find time T when SI=4000
And she has a principal amount, P=Rs. 15000

And the rate for simple interest is given as 8% in the question.
Now, $SI = \dfrac{{P \times R \times T}}{{100}}$
$\Rightarrow 4000 = \dfrac{{15000 \times 8 \times T}}{{100}} \\ \Rightarrow 4000 = 150 \times 8 \times T \\ \Rightarrow T = 3.33 \\$
Hence, the required time when she will be able to buy the TV is 3.33 years.

Note: Whenever we face such a question, the key concept for solving the question is to first find out the extra amount she needs as an interest, then apply the formula of simple interest to calculate the time after which she collects that amount of interest at the given rate.