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Sequences and Series Ncert Solutions Maths class 11th Maths Class 11th Sequence and Series

102. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

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Payal Gupta | Contributor-Level 10

4 months ago

102. Given, cost of scooter = ?22,000

Amount paid =? 4000

Amount unpaid =? 22,000 -? 4000 =? 18,000

Now, Number of installments =Amount unpaid/Amount of each instalment

As he per 10% interest on up unpaid amount and ?1000 each installment

Amount of 1st instalment =? 1000 +? $\frac{18000 \times 10 \times 1}{100}$ = ?1000 + ?1800 =? 2800

Amount of 2nd installment =? 1000 +? $\frac{(18000 - 1000) \times 10 \times 1}{100}$ =? 1000 +? 1700 =? 2700

Similarly,

Amount of 3rd installment =? 1000 +? $\frac{(17000 - 1000) \times 10 \times 1}{100}$ =? 1000 +? 1600 =? 2600

So, Total installment paid =? 2800 +? 1600 =? 2600 + …… upto 18 installment

$= \frac{18}{2} [2 \times 2800 + (18 - 1) (- 100)]$

= 9 [5600 - 1700]

= 9 × 3900

=? 35,000

Total cost of scooter = Amoun

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102. Given, cost of scooter = ?22,000

Amount paid =? 4000

Amount unpaid =? 22,000 -? 4000 =? 18,000

Now, Number of installments =Amount unpaid/Amount of each instalment

As he per 10% interest on up unpaid amount and ?1000 each installment

Amount of 1st instalment =? 1000 +? $\frac{18000 \times 10 \times 1}{100}$ = ?1000 + ?1800 =? 2800

Amount of 2nd installment =? 1000 +? $\frac{(18000 - 1000) \times 10 \times 1}{100}$ =? 1000 +? 1700 =? 2700

Similarly,

Amount of 3rd installment =? 1000 +? $\frac{(17000 - 1000) \times 10 \times 1}{100}$ =? 1000 +? 1600 =? 2600

So, Total installment paid =? 2800 +? 1600 =? 2600 + …… upto 18 installment

$= \frac{18}{2} [2 \times 2800 + (18 - 1) (- 100)]$

= 9 [5600 - 1700]

= 9 × 3900

=? 35,000

Total cost of scooter = Amount + Total installment paid

=? 4000 +? 35,100

=? 39100

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102. Given, cost of scooter = ?22,000Amount paid =? 4000Amount unpaid =? 22,000 -? 4000 =? 18,000Now, Number of installments =Amount unpaid/Amount of each instalment As he per 10% interest on up unpaid amount and ?1000 each installmentAmount of 1st instalment =? 1000 +?  <math><mrow><mfrac><mrow><mn>1</mn><mn>8</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo>×</mo><mn>1</mn><mn>0</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math> = ?1000 + ?1800 =? 2800Amount of 2nd installment =? 1000 +?  <math><mrow><mfrac><mrow><mo stretchy="false"> (</mo><mn>1</mn><mn>8</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo>−</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo stretchy="false">)</mo><mo>×</mo><mn>1</mn><mn>0</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0 </mn></mrow></mfrac></mrow></math>=? 1000 +? 1700 =? 2700Similarly, Amount of 3rd installment =? 1000 +?  <math><mrow><mfrac><mrow><mrow><mo> (</mo><mrow><mn>1</mn><mn>7</mn><mn>0</mn><mn>0</mn><mn>0</mn><mo>−</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow><mo>)</mo></mrow><mo>×</mo><mn>1</mn><mn>0</mn><mo>×</mo><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn><mn>0</mn></mrow></mfrac></mrow></math> =? 1000 +? 1600 =? 2600So, Total installment paid =? 2800 +? 1600 =? 2600 + …… upto 18 installment<math><mrow><mo>=</mo><mfrac><mrow><mn>1</mn><mn>8</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo stretchy="false"> [</mo><mn>2</mn><mo>×</mo><mn>2</mn><mn>8</mn><mn>0</mn><mn>0</mn><mo>+</mo><mo stretchy="false"> (</mo><mn>1</mn><mn>8</mn><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false"> (</mo><mo>−</mo><mn>1</mn><mn>0</mn><mn>0</mn><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow></math>= 9 [5600 - 1700]= 9 × 3900=? 35,000Total cost of scooter = Amount + Total installment paid=? 4000 +? 35,100=? 39100

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102. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

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