7. Babubhai borrows Rs. 4000 and agrees to repay with a total interest of Rs. 500. in 10 instalments, each instalment being less that the preceding instalment by Rs. 10. What should be the first and the last instalment?
Sol. Total money repaid by Babubhai in 10 instalments = (S10)= Principle + Interest
∴ S10 = 4000 + 500
∴ S10 = Rs. 4500
No. of instalments (n) = 10
∵ He repays each instalment being less that the preceding instalment by Rs. 10.
∴ Difference between two consecutive instalments (d) = – 10
First instalment = (a) = ?
Last instalment (t10) = ?
Sn = n/2[2a + (n – 1) d]
∴ S10 = 10/2 [2a + (10 – 1) d]
∴ 4500 = 5 [2a + 9 (– 10)]
∴ 4500/5 = 2a – 90
∴ 900 = 2a – 90
∴ 900 + 90 = 2a
∴ 990 = 2a
∴ a = 990/2
∴ a = 495 ............. eq. (i)
Now, tn = a + (n – 1) d
∴ t10 = a + (10 – 1) d
∴ t10 = 495 + 9 (– 10) [From eq. (i)]
∴ t10 = 495 – 90
∴ t10 = 405
∴ First instalment is Rs. 495 and last instalment is Rs.405
