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?

Amount Paid to buy scooter = Rs. 22,000

Shamshad Pays Cash = Rs. 4000

Remaining Balance = Rs. (22000 - 4000) = 18000

Annual Instalment = Rs 1000 + interest@10% on unpaid amount

1st Instalment

Unpaid Amount = Rs. 18000

Interest on Unpaid Amount = (10/100) × 18000 = 1800

Amount of Instalment = Rs. 1000 + Rs. 1800 = Rs. 2800

2nd Instalment

Unpaid Amount = Rs. (18000 - 1000) = Rs. 17000

Interest on Unpaid Amount = (10/100) × 17000 = 1700

Amount of Instalment = Rs. 1000 + Rs. 1700 = Rs. 2700

3rd Instalment

Unpaid Amount = Rs. (17000 - 1000) = Rs. 16000

Interest on Unpaid Amount = (10/100) × 16000 = 1600

Amount of Instalment = Rs. 1000 + Rs. 1600 = Rs. 2600

Total no. of Instalments = 18000/1000 = 18

Thus, Annual Instalments are 2800, 2700, 2600, …upto 18 terms

Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.

Here

first term(a) = 2800

Common difference(d) = 2700 - 2800 = - 100

Number of terms(n) = 18

Total amount paid in 12 instalments is given by -

S_n = (n/2)[2a + (n - 1)d]

∴ S₁₈ = (18/2)[2(2800) + (18 - 1)( - 100)]

= 9[5600 + 17( - 100)]

= 9[5600 - 1700]

= 9 × 3900

= 35100

Hence, total amount paid in 12 Instalments = Rs 35100

Hence,

Total Cost of Tractor

= Amount paid earlier + Amount paid in 12 Instalments

= Rs. (4000 + 35100)

= Rs. 39100