Q4 of 23 Page 1

Attempt any two sub-questions from the following:

Babubhai borrows 4,000 and agrees to repay with a total interest of 500 in 10 instalments, each instalment being less than the preceding instalment by 10, should be the first and last instalments?

Total money repaid by Babubhai in 10 instalments = S10

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 ............. (1)


Now, tn = a + (n – 1) d


∴ t10 = a + (10 – 1) d


∴ t10 = 495 + 9 (– 10) [From (1)]


∴ t10 = 495 – 90


∴ t10 = 405


∴ First instalment is Rs. 495 and last instalment is Rs.405


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