Question

a person buys a bike by way of loan. he clears the loan in 10 increased installment. every month he remits the installment by adding a particular sum the preceding installment. if the sum of 3rd and 9th installment if rupees 15000 and sum of 2nd and 6th installments is rupees 13000 find last installment amount and the total amount remitted by him​

Answer 1

His last payement was of Rs. 9000 and the total was Rs. 72500.

Step-by-step explanation:

n3 + n9 = 15000

n2 + n6 = 13000

Since in every payment the person adds a particular sum, let x be that particular sum, then, n3 = n1 + x + x = n1 + 2x and so on.

Thus:

n3 + n9 = n1 + 2x + n1 + 8x = 2n1 + 10x

⇒2n1 + 10x = 15000

n2 + n6 = 2n1 + 6x

⇒2n1 + 6x = 13000 ⇔ n1 = 6500 - 3x

Returnung to the previous equation:

2n1 + 10x = 15000 ⇔ 2(6500 - 3x) + 10x = 15000

⇔ 13000 - 6x + 10x = 15000

⇔ 4x = 2000

⇔ x = 500

Let T be the total price he payed.

Now, we know that he payed it in 10 times, then:

n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9 + n10 = T

⇔ n1 + n2 + n3 + n1 + 3x + n1 + 4x + n6 + n1 + 6x + n1 + 7x + n9 + n1 +9x = T

⇔ 6n1 + n2 + n6 + n3 + n9 + 29x = T

⇔ 6(6500 - 3x) + 13000 + 15000 + 29x = T

⇔ 39000 - 18x + 28000 + 29x = T

⇔ 67000 + 11 x 500 = T

⇔ T = Rs. 72500

To know the last installment we just need to compute:

n9 = n1 + 8x = 6500 - 3x + 8x = 6500 - 3 x 500 + 8 x 500 = Rs. 9000

Hence, his last installment was of Rs. 9000 and the total was Rs. 72500.