A person pay a loan of rupees 45750 in monthly installments each installment being more than the former by rupees 50. the amount of first installment is rupees 800. In how many installments will the entire amount be paid? Give reasons.

An equation can be set up as: 45,750 = 50x + 800

x representing each installment

We can simplify this by subtracting 800 and dividing by 50:

44,950 = 50x

899 = x

The entire amount will be paid in 900 installments.

Step-by-step explanation:

Step 1: Given first installment = Rs 800. Each installment is 50 more than the former. So this forms an arithmetic progression and the last term is 45750 when the loan is repaid.

⇒ 800, 850, 900, ... 45750

So a = 800, d = 50 and a (n) = 45750

Find number of installments, n using the equation for last term, a (n) = a + (n-1) d

⇒ 45750 = 800 + (n - 1) 50

⇒ 44950 = 50n - 50

⇒ 50n = 45000

⇒ n = 900