Question

Question 28 Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Class X1 - Maths -Sequences and Series Page 200

Answer 1

Scooter cost = 22000 ₹
down payment = 4000₹
rest payment = 22000 - 4000
= 18000 ₹

Now, interest on 1st installment = P × R × T/100
= 18000 × 10 × 1/100
= 1800₹
unpaid amount = 18000 - 1000 = 17000₹
interest on 2nd installment = P × R × T /100
= 17000 × 10 × 1/100
= 1700₹
unpaid amount = 17000 - 1000 = 16000₹
interest on 3rd installment = P × R × T/100
= 16000 × 10 × 1/100
= 1600₹
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Total interest paid by him = 1800 + 1700 + 1600 + ..... + 18 terms
Here,
first term {a } = 1800
common difference ( d ) = -100
Sum of 18 terms = 18/2{ 2 × 1800 + (18 -1) × 100}
= 9 { 3600 - 1700}
= 9 × 1900
= 17100₹

Hence, actual cost of scooter = 22000₹ + 17100₹
= 39100₹