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Question
Babubhai borrows Rs. 4,000 and agrees to repay with a total interest of Rs. 500 in 10 installments, each installment being less than the preceding installment by Rs. 10. What should be the first and the last installments?
Solution
Each installment is Rs. 10 less than the preceding one.
∴ The installments are in A.P. with a common difference - 10
Babubhai repays Rs. 4000 with the interest of Rs. 500 in 10 installments
i.e. S10 =4000 + 500= 4500
Here n = 10, 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 installment is Rs. 495 and the last installment is Rs. 405.
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