Question

A person pays rs. 975 in monthly installment such that each installment is less than the earlier instalment by rs. 5 .If he first instalment is rs.100in what time will the entire amount be paid?

Answer 1

$\huge\blue{Heya!!!\:Mate }$

As given in problem, A=100, D=-5

Formula is:

Sum of AP = n/2 [2a+(n-1)d]

Therefore, 

975 = n/2 [200+(n-1)-5]

1950 = n(200-5n+5)

1950 = 205n-5n^2

5n^2-205n+1950 = 0

n^2-41n+391 = 0

n^2-26n-15n+390 = 0

n(n-26) - 15(n-26) = 0

Hence,

n = 15 or 26.

So,

n = 15 months.

Answer 2

Step-by-step explanation:

As given in problem, A=100, D=-5

Formula is:

Sum of AP = n/2 [2a+(n-1)d]

Therefore, 

975 = n/2 [200+(n-1)-5]

1950 = n(200-5n+5)

1950 = 205n-5n^2

5n^2-205n+1950 = 0

n^2-41n+391 = 0

n^2-26n-15n+390 = 0

n(n-26) - 15(n-26) = 0

Hence,

n = 15 or 26.

So,

n = 15 months.