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?

Answer 1

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,

${\displaystyle S_n=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]}$

${\displaystyle S_{10}=4500=\frac{10}{2}[2\text{a}+(10-1)(-10)]}$

∴ 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.

${\displaystyle {\text{t}}_{\text{n}}=\text{a}+(\text{n}-1)\text{d}}$

${\displaystyle {\text{t}}_{10}=495+(10-1)\times (-10)}$

${\displaystyle {\text{t}}_{10}=495+9\times (-10)}$

${\displaystyle {\text{t}}_{10}=495-90}$

${\displaystyle \therefore {\text{t}}_{10}=405}$

The first installment is Rs. 495 and the last installment is Rs. 405.