Question

any person borrows rupees 4000 and agrees to repay with the total interest of rupees 500 in 10 installments each installment being less than the preceding installment by rupees 10 what should be the first and last installment

Answer 1

Step-by-step explanation:

Given a person borrows rupees 4000 and agrees to repay with the total interest of rupees 500 in 10 installments each installment being less than the preceding installment by rupees 10 what should be the first and last installment

• Given total amount + interest = 4000 + 500 = Rs 4500 = Sn
• Now d = - 10 (since preceding by Rs 10 ) and n = 10
• We know that
• Sum Sn = n / 2 (2a + (n – 1)d )
• 4500 = 10/2 (2a + (10 – 1) - 10)
• 450 x 2 = (2a – 90)
• 900 = 2a – 90
• 2a = 990
• Or a = 495
• So we get first instalment as Rs 495
• Now tn = a + (n – 1)d
• So t 10 = 495 + (10 – 1) (- 10)
• = 495 – 90
• = Rs 405
• Therefore last instalment will be Rs 405

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Answer 2

The first installment is Rs. 495 and the last installment is Rs. 405.

Step-by-step explanation:

Let the first installment is Rs. x, then the next installment will be Rs. (x - 10) and that goes on for ten times as the total number of installment is 10.

So, x + (x - 10) + (x - 20) + ....... up to ten terms = (4000 + 500)

⇒ $\frac{10}{2}[2x - (10 - 1)\times 10] = 4500$

{Since this is a sum of A.P. series and has first term x, common difference 10 and the number of terms 10}

⇒ 2x = 990

⇒ x = 495

Hence, (x - 90) = 495 - 90 = 405

Therefore, the first installment is Rs. 495 and the last installment is Rs. 405. (Answer)