Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 instlments, each instalment being less than the preceding instalment by Rs. 10. What should be the first and the last instalments?
Solution
Each instalment is Rs. 10 less than the preceding one.
∴ The instalments are in A.P. with a common difference - 10
Babubhai repays Rs. 4000 with interest of Rs. 500 in 10 instalments
i.e. S10 =4000 + 500= 4500
Here n = 12, d = 10 and S10 = 4500.
we have to find the 1st instalment i.e. a,
`S_n = "n"/2[2"a" + ("n"-1)"d"]`
`S_10 = 4500 = 10/2[2"a" + (10-1)(-10)]`
∴ 4500 = 5[2a + 9x(-10)]
∴ 4500/5 = [2a + 9x(-10)]
∴ 900 = 2a - 90
∴2a = 900 + 90 = 990
∴a = 990/2 = 495
∴a = 495
tn = last instalment.
`"t"_"n" = "a" + ("n" - 1)"d"`
`"t"_10=495+(10-1)xx(-10)`
`"t"_10=495+9xx(-10)`
`"t"_10=495-90`
`therefore "t"_10=405`
The first instalment is Rs. 495 andthe last instalment is Rs. 405.
