Question

A person buys a bike by way of loan. He clears the loan in 10 inereased instalments. Everymonth he remits the instalment by adding a particular sum the preceding instalment. If thesum of 3rd and 9th instalments if Rs. 15000 and sum of 2nd and 6th instalments is Rs. 13000,Find last instalment amount and the total amount remitted by him.

Answer 1

Answer:

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.

Answer 2

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