Shamshad Ali buys a scooter for Rs 22000 . He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Solution:

It is given that Shamshad Ali buys a scooter for Rs 22000 and pays Rs 4000 in cash.

Hence, unpaid amount in Rs = 22000 - 4000 = 18000

According to the given condition, the interest paid annually is

(10% of 18000), (10% of 17000), (10% of 16000), ... , (10% of 1000)

Thus, total interest to be paid

= (10% of 18000) + (10% of 17000) + .... + (10% of 1000)

= 10% of (18000 + 17000 + .... + 1000)

= 10% of (1000 + 2000 + .... + 18000)

Now, the series 1000 + 2000 + .... + 18000 forms an A.P. with a and d both equal to 1000.

Let the number of terms of the A.P. be n.

Therefore,

⇒ aₙ = a + (n - 1) d

⇒ 18000 = 1000 + (n - 1)(1000)

⇒ 18000 - 1000 = 1000 (n - 1)

⇒ n - 1 = 17000/1000

⇒ n = 17 + 1

⇒ n = 18

Using the sum of A.P. formula,

Sₙ = n/2 [2a + (n - 1) d]

S₁₈ = 18/2 [2 (1000) + (18 - 1)(1000)]

= 9[2000 + 17000]

= 9 x 19000

= 171000

Therefore, total interest to be paid is

10% of (1000 + 2000 + .... + 18000)

= 10% of 171000

= 10/100 x 171000

= 17100

Now, total cost of scooter in Rs = 22000 + 17100 = 39100

Thus, the scooter will cost him Rs 39100

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NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 28

Shamshad Ali buys a scooter for Rs 22000 . He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

Summary:

The scooter was initially bought for Rs 22000, he agreed to pay Rs 1000 plus 10% interest on the unpaid amount, then the scooter cost him Rs 39,100