Question

A person plans to clear his debt of rs. 3600 in 40 instalments which are in



a.P. He dies after clearing 30 instalments leaving one third of his debt. Find the amount of the first instalment

Answer 1

One manages to repay his 3600 debt in 40 installments in the Samanthar range, which he then dies after installing in 30 installments .If the debt is not repayable, then pay the first installment

Answer 2

Explanation:

Let  us consider “d” as the common difference

In this case the installments are : a, a + d, a + 2d ………..40th term

nth term of AP, tn = a + (n – 1)d

⇒ t40 = a + (40 – 1)d  = a + 39d

Sum of n term of A

Given total debt = Rs 3600

⇒ 20[2a + 39d] = 3600

2a + 39d = 180 → (1)

The case also shows that 30 installments have been

And the unpaid amount = one-third of Rs 3600 = Rs 1200

Hence, total payment till 30 installments = 3600 – 1200  

                                                                   = Rs 2400

     = 15(2a + 29d)

⇒ 15(2a+29d) = 2400

2a +29d = 160 → (2)

Subtract (2) and (1), we get

2a + 39d = 180

2a +29d = 160

--------------------

       10d = 20

∴ d = 2

Put d = 2 in equation (1)

2a + 29(2) = 180

⇒ 2a + 58 = 180

⇒ 2a = 180 – 58 = 122

∴ a = 61

8th installment, t8 = a + 7d

= 61 + 7(2)

= 61 + 14 = 75