Rohit took a loan of Rs 22000 from a bank to buy a television. He paid Rs 6000 as down payment and agreed to pay the rest amount in installments. As his first installment he agreed to pay Rs 400 and then will increase the payment by Rs 200 every month till all the money is paid.
1. Does the installment form an AP? Why?
2. Write the first term and common difference of the AP so formed.
3. How many months will Rohit take to clear his loan?
4. What is the total amount paid by Rohit to buy the Television?
Answers
Given : Rohit took a loan of Rs 22000 from a bank to buy a television. He paid Rs 6000 as down payment and agreed to pay the rest amount in installments
his first installment he agreed to pay Rs 400 and then will increase the payment by Rs 200 every month till all the money is paid.
To Find : 1. Does the installment form an AP? Why?
2. Write the first term and common difference of the AP so formed.
3. How many months will Rohit take to clear his loan?
4. What is the total amount paid by Rohit to buy the Television?
Solution:
Rohit took a loan of Rs 22000 from a bank to buy a television
He paid Rs 6000 as down payment
Total amount of TV = 22000 + 6000 = Rs 28000
First installment he agreed to pay Rs 400 and then will increase the payment by Rs 200 every month till all the money is paid.
Yes this form an AP
as difference in consecutive installment is same = 200
First Term = a = 400
common difference = 200
Let say Rohit take n months
Total to be paid = rs 22000 ( assuming loan interest free)
Sn = (n/2) (2a + (n-1)d)
22000 = (n/2) (2*400 + (n - 1)200)
=> 22000 = n( 400 + 100n - 100)
=> 220 = n ( 3 + n)
=> n² + 3n - 220 = 0
Does not get integral values of n
approx. n = 14
May be mistake in data.
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