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

Solution:

It is given that farmer pays Rs 6000 in cash.

Hence, unpaid amount in Rs = 12000 - 6000 = 6000

According to the given condition, the interest paid annually is

(12% of 6000), (12% of 5500), (12% of 5000), ...., (12% of 500)

Thus, total interest to be paid = 12% of 6000 + 12% of 5500 + .... + 12% of 500

= 12% of (6000 + 5500 + .... + 500)

= 12% of (500 + 1000 + .... + 6000)

Now, the series 500 + 1000 + .... + 6000 forms an A.P. with a and d both equal to 500.

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

Therefore,

⇒ aₙ = a + (n - 1) d

⇒ 6000 = 500 + (n - 1)(500)

⇒ 6000 - 500 = 500(n - 1)

⇒ n - 1 = 5500/500

⇒ n - 1 = 11

⇒ n = 12

Sₙ = n/2 [2a + (n - 1) d]

S₁₂ = 12/2 [2 (500) + (12 - 1)(500)]

= 6 [1000 + 5500]

= 6 x 6500

= 39000

Therefore, total interest to be paid is

12% of (500 +1000 + .... + 6000)

= 12% of 39000

= 12/100 x 39000

= 4680

Now, total cost of tractor = 12000 + 4680 = Rs 16680

Thus, the tractor will cost him Rs 16680

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 27

Summary:

The cost of the tractor considering the annual instalment of ₹ 500 and then the 12% interest over the unpaid amount is Rs16680

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