101. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

101. Given,

cost of tractor =? 12,000

Amount paid =? 62,000

Amount unpaid =? 12000 -? 6000 =? 6000

So, number of instalments =     

 

$=$ ?  $\frac{6000}{500}$

= 12 = n

Now, interest on 1st installment = interest on unpaid amount ( i.e.? 6000) for 1 Year.

=?  $\frac{6000\times 12\times 1}{100}$ = ?720

Similarly,

Interest on 2nd installment = interest on (? 6000 -? 500) for the next 1 year

=?  $\frac{5500\times 12\times 1}{100}$ = ?660

And,

Interest on 2nd installment =?  $\frac{(5500-500)\times 12\times 1}{100}$

=? 600

Here, Total (interest per) installment paid =? (720 + 660 + 600 + ……. upto 12 terms)

$=\frac{12}{2}[2(720)+(12-1)(-60)]$  { $?$ 720 + 660 + 600 …….is an A.P. of a = 720, d = 660 - 720 

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101. Given,

cost of tractor =? 12,000

Amount paid =? 62,000

Amount unpaid =? 12000 -? 6000 =? 6000

So, number of instalments =     

 

$=$ ?  $\frac{6000}{500}$

= 12 = n

Now, interest on 1st installment = interest on unpaid amount ( i.e.? 6000) for 1 Year.

=?  $\frac{6000\times 12\times 1}{100}$ = ?720

Similarly,

Interest on 2nd installment = interest on (? 6000 -? 500) for the next 1 year

=?  $\frac{5500\times 12\times 1}{100}$ = ?660

And,

Interest on 2nd installment =?  $\frac{(5500-500)\times 12\times 1}{100}$

=? 600

Here, Total (interest per) installment paid =? (720 + 660 + 600 + ……. upto 12 terms)

$=\frac{12}{2}[2(720)+(12-1)(-60)]$  { $?$ 720 + 660 + 600 …….is an A.P. of a = 720, d = 660 - 720  = - 60}

= 6 [ 1440 - 660]

= 6 × 780

=? 4680

So, the total cost of tractor = cost price + installments

=? 12,000 +? 4680

=? 16680

less

<p><strong>101.&nbsp;</strong>Given, </p><p>cost of tractor =? 12,000</p><p>Amount paid =? 62,000</p><p>Amount unpaid =? 12000 -? 6000 =? 6000</p><p>So, number of instalments&nbsp;<span title="Click to copy mathml">=&nbsp; &nbsp; &nbsp;</span></p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1729836181phpq3t5U1_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1729836181phpq3t5U1.jpeg" alt="" width="" height=""></picture></div></div><p>&nbsp;</p><p><span title="Click to copy mathml"><math><mrow><mo>=</mo></mrow></math></span>&nbsp;? &nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>6</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow><mrow><mn>5</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></span></p><p>= 12 = n</p><p>Now, interest on 1st installment = interest on unpaid amount ( i.e.? 6000) for 1 Year.</p><p>=? &nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>6</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>2</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></span>&nbsp;= ?720</p><p>Similarly, </p><p>Interest on 2nd installment = interest on (? 6000 -? 500) for the next 1 year</p><p>=? &nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mn>5</mn><mn>5</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>2</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></span>&nbsp;= ?660</p><p>And, </p><p>Interest on 2nd installment =? &nbsp;<span title="Click to copy mathml"><math><mrow><mfrac><mrow><mo stretchy="false"> (</mo><mn>5</mn><mn>5</mn><mn>0</mn><mn>0</mn><mo>−</mo><mn>5</mn><mn>0</mn><mn>0</mn><mo stretchy="false">)</mo><mo>×</mo><mn>1</mn><mn>2</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math></span></p><p>=? 600</p><p>Here, Total (interest per) installment paid =? (720 + 660 + 600 + ……. upto 12 terms)</p><p><span title="Click to copy mathml"><math><mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo stretchy="false"> [</mo><mn>2</mn><mo stretchy="false"> (</mo><mn>7</mn><mn>2</mn><mn>0</mn><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false"> (</mo><mn>1</mn><mn>2</mn><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false"> (</mo><mo>−</mo><mn>6</mn><mn>0</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></math></span>&nbsp; {&nbsp;<span title="Click to copy mathml"><math><mrow><mo>? </mo></mrow></math></span> 720 + 660 + 600 …….is an A.P. of a = 720, d = 660 - 720&nbsp; = - 60}</p><p>= 6 [ 1440 - 660]</p><p>= 6 × 780</p><p>=? 4680</p><p>So, the total cost of tractor = cost price + installments</p><p>=? 12,000 +? 4680</p><p>=? 16680</p>

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