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Home » A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
CBSE | Class 11 | Maths | Miscellaneous Exercise | NCERT | Sequences and Series
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?

Given, the rancher pays Rs 6000 in real money.

 

In this way, the neglected sum

    \[=\text{ }\mathbf{Rs}\text{ }\mathbf{12000}\text{ }\text{ }\mathbf{Rs}\text{ }\mathbf{6000}\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{6000}\]

From the inquiry, the interest paid every year will be

 

    \[\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{6000},\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5500},\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5000},\text{ }\ldots \text{ },\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{500}\]

Subsequently, the absolute premium to be paid

    \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{6000}\text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5500}\text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{5000}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{500}\]

 

    \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{6000}\text{ }+\text{ }\mathbf{5500}\text{ }+\text{ }\mathbf{5000}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{500} \right)\]

    \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{500}\text{ }+\text{ }\mathbf{1000}\text{ }+\text{ }\mathbf{1500}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{6000} \right)\]

It’s seen that, the series

    \[\mathbf{500},\text{ }\mathbf{1000},\text{ }\mathbf{1500}\text{ }\ldots \text{ }\mathbf{6000}\text{ }\mathbf{is}\]

an A.P. with the initial term and normal contrast both equivalent to

    \[\mathbf{500}.\]

How about we take the quantity of terms of the A.P. to be n.

 

In this way,

    \[\mathbf{6000}\text{ }=\text{ }\mathbf{500}\text{ }+\text{ }\left( \mathbf{n}\text{ }\text{ }\mathbf{1} \right)\text{ }\mathbf{500}\]

    \[\mathbf{1}\text{ }+\text{ }\left( \mathbf{n}\text{ }\text{ }\mathbf{1} \right)\text{ }=\text{ }\mathbf{12}\]

    \[\mathbf{n}\text{ }=\text{ }\mathbf{12}\]

Presently,

 

The amount of the

    \[\mathbf{A}.\mathbf{P}\text{ }=\text{ }\mathbf{12}/\mathbf{2}\text{ }\left[ \mathbf{2}\left( \mathbf{500} \right)\text{ }+\text{ }\left( \mathbf{12}\text{ }\text{ }\mathbf{1} \right)\left( \mathbf{500} \right) \right]\text{ }=\text{ }\mathbf{6}\text{ }\left[ \mathbf{1000}\text{ }+\text{ }\mathbf{5500} \right]\text{ }=\text{ }\mathbf{6}\left( \mathbf{6500} \right)\text{ }=\text{ }\mathbf{39000}\]

 

Subsequently, the absolute premium to be paid

    \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\left( \mathbf{500}\text{ }+\text{ }\mathbf{1000}\text{ }+\text{ }\mathbf{1500}\text{ }+\text{ }\ldots \text{ }+\text{ }\mathbf{6000} \right)\]

 

    \[=\text{ }\mathbf{12}%\text{ }\mathbf{of}\text{ }\mathbf{39000}\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{4680}\]

Subsequently, the work vehicle will cost the rancher

    \[=\text{ }\left( \mathbf{Rs}\text{ }\mathbf{12000}\text{ }+\text{ }\mathbf{Rs}\text{ }\mathbf{4680} \right)\text{ }=\text{ }\mathbf{Rs}\text{ }\mathbf{16680}\]

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