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. S_{10} =4000 + 500= 4500

Here n = 12, d = 10 and S_{10} = 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

t_{n }= 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.